How To Graph A linear Function?

Question

How do you graph y= -2x+3?

I do not know where to start. My professor was getting so mad at us. I went outside and cried. I, in no way understand even the basics. Can someone explain about the pairs I am suppose to have to graph this with. Thank you in advance.

Answer 1

Y=mx+B

m= slope

B= y-intercept

X= horizontal (Indepentent ex Time)
Y= Vertical (Dependent ex. Distance)

You start at the y-intercept (B), which is always when X=0. In this case in that situation you start at Y=3 (B), So from zero on the X axis go up 3 units.(Now to m) -2 is the slope. -2/1 = -2 they are the same thing. For the number on top you move up or down, since it is negative you will move down. For the number on bottom you will move right. So you move down 2 and over 1. If it was 3/4ths you would move up 3 and right 4. You always move right because you are always graphing things from the past to the present.

Answer 2

Don't worry! The linear function is not that hard.

First, draw a coordinate system.

Now, look at your function y = -2x+3. If you insert any number in x's place, you get a value for y. For example, inserting 0 (zero) in x's place gives you y = (-2)*0 + 3 = 3. So your first coordinate pair is (x,y) = (0,3) because when x = 0, y = 3.

Plot your first point in the coordinate system. Go 3 units up the y axis, and make a mark. That's your first point.

Calculate your next pair. Let's say x = 1. Then y = -2*(1) + 3 = 1, so when x = 1, y = 1. Your second point is (x,y) = (1,1). Plot that in your coordinate system.

The third point is x = 2. So y = (-2)*2 +3 = -1. When x = 2, y = -1, so (x,y) = (2,-1). Plot this point in your coordinate system.

The three points you've plotted so far lie on a straight line. If you connect these points, you'll have a line that intersects the y axis at 3, and has a slope of -2 (every time you go 1 unit to the right, you go two units down. (Down because the slope is MINUS 2)).

Once you become accustomed to linear functions, you will be able to see this much easier. The number that gets multiplied with x is always the line's slope (-2 in your case), and the number that gets added (3 in your case) is always the line's intercept with the y axis.

Hope this helps. You can do it!

Answer 3

Let's start with something simpler.

y = 2x

It's linear because there are no terms with xy together or a power of x or y. Linear = it will graph to a straight line.

SO let's plug in some numbers.
if x = 0, then 2x (which is what y equals) is 0.
if x = 1, then 2x is 2.

Remember, y = 2x means "for the y value, use twice whatever x is". SO
x = 2 then y = 4
x = 3 then y = 6
x = 10 then y = 20
x = 1000 then y = 2000
and so on forever.

Since they're both positive, the points will all be in the upper right quadrant. X is horizontal and Y is vertical. You can see examples of the empty graph in your text. Notice the two lines (axes) cross. The point where they cross is x = 0 and y = 0. That's one of your points! Make a dot there. Now go to the right from there and find 1 (x = 1). Then move your pencil up two lines (that's where y = 2). That's also on your graph! Put a dot there.

Two dots is enough for a graph. Put a straight line through those two running past the dots in both directions. It will be a straight line at about this angle: /

If you move your pencil across the horizontal axis to 2 (x = 2) and then move up it *better* cross your line at the 4th line up (y = 4).

I hope you're still with me.

Your graph is a bit more complex, but not too much.

Pick a few values for x (like 0, 1, 2) and plug it in and see what y equals.

x = 0, then -2x = 0 and -2x+3 = 3
x = 1, then -2x = -2 and -2x+3 = 1
x = 2, then -2x = -4 and -2x+3 = -1

More complex because of the +3 and that darn minus sign. The easy answers cross through two quadrants!

Make a mark at x = 0 and y = 3
Make another at x = 1 and y = 1

Draw a line between them, extending in either direction. You'll get a line at about this angle: \

Our third point is x = 2 and y = -1 (below the vertical axis). This point had BETTER be on your line!

If it is, you're getting it. Send me $100 for a tutoring lesson. :))))

Answer 4

It sounds like you need to know how to figure out how to get the points. You need to make an xy chart. Some people call it a T chart. You need to pick three numbers for X, then substitute each of those into your equation. You multiply by three then add one. Whatever your answer is, that's your y value. In this case, I pick the numbers 0, 1, & 2. When you substitute 0 for X, you get y=1 because: y = 3x + 1 y = 3 (0) + 1 y = 0 + 1 y = 1 When you substitute 1 for x, you get y=4 because: y = 3x + 1 y = 3(1) + 1 y = 3 + 1 y = 4 When you substitute 2 for x, you get y=7 because: y = 3x + 1 y = 3(2) + 1 y = 6 + 1 y = 7 So your xy chart should look like this: X, Y 0, 1 1, 4 2, 7 So the points you should graph is (0,1), (1,4), & (1,4). Hint: It should be a straight line. I don't know where you got (0,4), that point should not be on the graph.

Answer 5

Sorry to hear that.

The line is within the form Y = MX + C

i.e. The Y co'ord = The gradient (slope) x the x co'ord + the Y axis intercept.

So in this case the Y intercept is (0,3) because the y co'ord of the "C" part is 3.

The gradient of the line is -2, because that is the number in front of the x term.

To draw this:

Set up your axis, drawing a horizontal line for the x axis, and a vertical line for the y axis. Have them drawn in such a way as that you form an "X" turned on it's side.

Find where the 2 lines cross, this is called the origin ("O" for short).

From the O measure up three divisions on the graph paper, this the point (0,3).

To find other points it is simply a case of putting in different values of X and finding what the Y co'ord is.

I'll give you some to help you.

(1,1)

(-1,5)

(-2,7)

Plot these points on the graph by going along the x axis for the first co,ord point, and up the way for the second point.

e.g. (3,-3)
/ \
first co'ord point second co'ord point


After you've plotted the points, just join the dots in a straight line.

Hope this helps!

Answer 6

The set of numbers that you substitute for x is called the domain, the numbers that you get for y is the range. Suppose you let x=1, then y would also be 1. If x=3, then y would be -3. Every time you pick a value for x you will get a corresponding value for y. These are the ordered pairs that you are going to graph. So far we have the ordered pairs (1,1) and (3, -3). If you plot them on an x-y plain you will have two points. Take a ruler and draw a line through the two points and you just graphed the function. There is always the possibility of making an error in math, so find one more ordered pair to see if it falls on that same line. You can pick any value for x, so pick an easy one.

Answer 7

Well you could graph this two ways. The easiest way is slope-int form

The number in front of x is the slope. So in this problem -2.
The number by itselft is the y intercept (where it crosses the y axis). so in this problem 3.

First plot the y intercept. You go up 3 on the y axis (vertical axis)
Then use the slope to plot the next point. From the point you just plotted, you go down 2 because it is negative and then 1 to the right because the slope is -2/1.
Then just draw your line.

The other way is to pick some points for x, lets say
-2, -1, 0 , 1, 2. Put these numbers in for x and find out what y is.
y = -2(-2) + 3 = 7
So we would plot the point (-2, 7). then repeat for -1, 0 , 1, 2

Answer 8

***********A PICTURE IS WORTH A THOUSAND WORDS***********

You can figure out the slope and the y intercept...other people and your textbook will give you that information, but the QUICKEST way to graph it is to choose a few values for x and calculate y.

x = 0___Substitute 0 into the equation: y = -2(0) + 3 ==> y = 3.

x = 1___Substitute 1 into the equation: y = -2(1) + 3 ==> y = 1.

x = 2___Substitute -1 into the equation: y = -2(2) + 3==>y = -1.

Write your pairs (points) from above: (0,3)____(1,1)____(2,-1)
and put those points onto your graph.

Once you can see the graph, you can also see the slope and the y-intercept and all that. Good luck!

***********A PICTURE IS WORTH A THOUSAND WORDS***********

Answer 9

Hey friend, its very easy, let me tell you,

since y= -2x+3
now what u do that consider any integer value of "x" randomly and try to get integer valu of "y".
first of all consider x=1; we'll get y=-2*1+3=-2+3=1
again consider x=4; we'll get y=-2*4+3=-8+3=-5

now take one more value let x= -2 ; y=-2(-2)+3=4+3=7

So we have
x = 1 4 -2
y= 1 -5 7

now i think u can draw the graph. just draw x-axis and y-axis take the value and corrosponding. and plot the graph
i hope u would have got the answer.
have a nice time!
Bikash Jain

Answer 10

Pick an x. Any x. Calculate y. That pair (x.y) is one of the points on the line.

Pick another x. Any x. Calculate its y. You now have two points. There's exactly one straight line that includes them. You're done.

Or you can pick y to suit yourself and calculate it's x.

The ideal choice of two points is to pick the one where x = 0 and the one where y = 0.

In this case, those points are (0,3) and (1.5, 0). If you don't know how to calculate those, review your algebra; until you have that much mastery over algebra, you're doomed to frustration in graphing algebraic equations.