Please help I don't understand how to do this problem?

Question

Write the equation of the line which passes through the point (2, 1) and is parallel to the line with equation y =5/2(fraction)x +6

Answer 1

Ok, all lines parallel to y = (5/2)X + 6 will be Y = (5/2)X + ?, that is, (5/2) X plus something. Lets call that something K.

So, Y = (5/2) X + K, and we know that it passes through (2,1), so when X = 2, Y = 1, so 1 = (5/2) * 2 + K, so K = -4, so the line is

Y = (5/2) X - 4

Answer 2

It has to have the same slope as the second equation. The slope is 5/2. So the parallel line is y=(5/2)x + C.

To solve for C, plug in x=2. The result (y) has to be 1. So (5/2)*2 + C must equal 1. Or 5 + C=1, making C equal -4.

The equation is y = (5/2)x - 4

Same slope, parallel (no intersection)

Answer 3

To find an equation of a line, you need a point and a slope. They give you point (2,1).
Use the other line, y = (5/2)x + 6, to find the slope.

Parallel lines have the same slope, so use the slope of this line.

y = (5/2)x + 6 is in the form of y = mx + b, where m = slope, so the slope is (5/2)

You now have (2,1) and m = 5/2
Use point-slope formula:

y - 1 = (5/2)(x - 2)

y = (5/2)x - 5 + 1
=(5/2)x - 4

Answer 4

ok. write down the original equation which is y= 5/2 x +6 if an the other line is paralell then u know that the slope has to be the same. standard form is y = mx+b m is ur slope and b is your y intercept. draw out a graph the first point should be (2,1) then use ur slope to graph the rest of the points. go up 5 over two then go down 5 over two again. in this case ur y intercept should come out to be a negative 4 and ur slope should be 5 /2 so your equation is gonna be y= 5 /2 x - 4.

Answer 5

y =5/2x +6

Equation of straight line is Y=MX+C, where M is the slope (gradiant) of the line. If two lines are parellel then they have the same slope, so the line passing through (2,1) will have M = 5/2. (increase in Y is 5 for every increase of 2 in X) You know one X and one Y value for points on the line because you've been given them in the question: Y=1, X=2, so now we know:

1 = 5/2*2 + C

As 5/2 * 2 = 5 we know
1 = 5 + C

rearranging:

1 - 5 = C

C = -4

so the equation is:

Y = 5/2X - 4

(assuming I've gotten that right, feel free to check it :D)

Answer 6

Since the equation has y by itself, it is in slope-intercept form, so its slope is the number in front of x, 5/2.

Now we can go to point-slope form, using 5/2 as slope and (2,1) for the point:

y-1=(5/2)(x-2)

Distribute: y-1=(5/2)x-5

then add 1: y= (5/2)x-4 This in the answer in slope-intercept form.

If the directions want standard form, multiply through by 2 and get the x and y terms together on one side:

2y=5x-3

5x-2y=3

Answer 7

well, since the other line will be parallel, it must have the same slope (5/2).
therefor the problem will start out as y=5/2x+b
plug in the coordinate (2,1) as shown: 1=5/2(2)+b
then solve for b...
1=5*2/2+b
1=5+b
-4=b
taking the new value for b we now have our equation:
y=5/2x-4