Write an equation of the line that passes through (3,7) and is parallel to the line show (1,4) and (-2,-2)

Answer 1

Hi Mariano!

In order to write the equation of the line that passes through (3,7) and is parallel to the line with points (1,4) and (-2,-2), we must first solve for the slope between (1,4) and (-2,-2).

We solve for the slope between those points because parallel lines have the same slope.

To solve for the slope we use the formula (y1–y2) ⁄ (x1–x2) .

Let us label (1,4) as (x1,y1) and (-2,-2) as (x2,y2).

Now plug the points into the slope formula: (4+2) ⁄ (1+2) = 6 ⁄ 3 = 2

Now that we have the slope, we can use the slope intercept formula (y = mx +b) and the (3,7) to determine the formula of the line.

m is the slope which we know must be 2

b is the y intercept, which we do not know yet, but will solve for

x and y are any coordinate point (x,y) on the line so in our case (3,7)

First let us plug in (3,7) and the slope (m=2) into y=mx+b.

7=2(3)+b

7=6+b (now subtract 6 on both sides of the equation)

1=b

Now that we have the y-intercept value, which is 1, all we have to do is plug in the value for b which is 1 and m which is 2.

m=2; b=1

y=mx+b

y=2x+1

Thus, your equation is y=2x+1.