Write an equation in slope intercept form.?

Question

Directions: Write an equation in slope intercept form for the line that satisfies each set of conditions.

1.) slope 0.25 passes through (0,4)
2.) passes through (-3, -1) parallel to the line that passes through (3,3) (0,6)

I don't have the first clue where to start with these, if you could work it and show me steps on how to get the answers. Thanks

Answer 1

The slope-intercept form for all linear equations is
y=mx + b. "m" is the slope of the line (it's the coefficient of the x term, along with the sign), and b is where the line, when graphed, cuts the y-axis. This happens b units above or below the origin, and the coordinates of that intercept are (0,b).

1.) slope 0.25 ,passes through (0,4)
Your equation is y=0.25x +4
You could have expressed the slope m as 1/4 if you so desired. y=(1/4)x +4
There is another way to find b as well. We shall see that way in your second question.

2.) passes through (-3,-1) parallel to the line that passes through (3,3) (0,6)
Once again, your equation is y=mx +b. What we need to get are values for m and b.
We know our desired line has the same slope as the line passing through (3,3)(0,6). And, we can find that line's slope.
Slope is a measure of steepness. It's the vertical height change over a specific horizontal distance. You probably know this as RISE / RUN. For the points (3,3)(0,6) Rise is 6-3, RUN is 0-3
Therefore m= RISE / RUN = (6-3)/(0-3)=3/-3 = -1
Our sought-after line therefore also has a slope of -1
and our equation is now y=-1x+b
Here is how we find b. We are told our line passes through (-3,-1). That means those values satisfy the equation y=-1x + b. I shall substitute -3 for x and -1 for y to get -1=-1(-3) +b
b=-4
My equation is therefore y = -x-4, and we're done.

Some extra tips to help you feel better about linear equations.
Tip 1- If you are going to put, or use, the slope-intercept form of the line, it is y=mx +b. The y must ALWAYS be +1y, alone on the left side.
Tip 2- A negative slope means that when graphed, the line leans to the left.
Tip 3- Lines that are parallel to one another have the same slope.
Tip 4- Lines that are perpendicular to one another have slopes that are the negative reciprocal of one another. If m of line 1= 3, the other line will have slope = -1/3
Good luck to you!

Answer 2

Slope-intercept form is y = mx + b where m = slope and b = y-intercept.
1. You are given your slope (m=0.25) and your x and y (0,4). Substitute these values into the equation to solve for b.
4 = 0.25(0) + b
4 = 0 + b
4 = b
So, your equation is y = 0.25x + 4

2. There's more work to do here. First, you have to find the equation for the line that passes through (3,3) and (0,6). Given two points, the first thing to find is the slope:
(6-3)/(0-3)
3/-3 = -1
The slope for this line is -1. Remember, that is the m in y=mx+b
Now, pick either (3,3) or (0,6). It does not matter which point you pick. I'm going to use (0,6). Remember, the x=0 and the y=6.
Substitute the m, x, and y to solve for b.
6 = (-1)(0) + b
6 = 0 + b
6 = b
So, the equation for the line that passes through (3,3) and (0,6) is y = -1x + 6 or y = -x +6

You're not finished!
Now, you need to know that parallel lines have the same slope. This means that the slope of the line passing through the point (-3, -1) is m = -1. You have x = -3 and y = -1 given to you, so substitute in to solve for b again.
-1 = (-1)(-3) + b
-1 = 3 + b Subtract 3 from both sides
-4 = b
The equation for the line parallel to your first line that will also pass through (-3, -1) is y = -1x - 4 or y = -x - 4.

To clean this up, your equations are:
y = -x + 6 and y = -x - 4

Answer 3

y-h = m (x-k)
(k, h) being a point on the slope, and m being the slope.

For the first question, change 0.25 to 1/4 for the slope, and then insert the numbers into the equation.
(k, h) = (0, 4)
m = 1/4
y-4 = 1/4*(x-0)
y= x/4 + 4

for the second, you need to figure out the slope with another equation. the slope is equal to that of a line parallel
m = (y2 - y1)/(x2 - x1)
(x1, y1) = (0, 6)
(x2, y2) = (3, 3)
m = (3 - 6)/(3 - 0)
m = -1
then use the other formula with (k, h) = (-3, -1)
y- (-1) = (-1)(x- (-3))
y + 1 = -(x+3)
y = -(x +4)

Answer 4

Use this formula: Y- y1 = m(X - x1)

So, slope .25.
Y - 4 = .25(X - 0)
Now isolate the y.
y = .25x + 4

For the second problem, find the slope. Use the following formula: (y2-y1)/(x2-x2) or (change of y)/(change of x)
(3-6)/(3-0) = 3/-3 or -1.
Now use the original formula.
y - 6 = -1(x - 0)
y = -x + 6

Answer 5

algebra fundemtals?

y=mx+b

line crosses the y axis at b


y=.25x+4

plug in a x point and you should solve for y



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