Slope Question

Question

The equation of a line through a given point, parallel to a second line. Assume that the line passes through the point (3,−1) and is parallel to the line through the points ( 1,3) and (−6,4).
Find the equation of this line in slope intercept form.

Answer 1

First solve for slope using the line you have 2 points for.

 

slope= ΔY/ΔX =(4-3)/-6-1 = (1/-7)= m

 

Because the second line is parallel to this they will have the same slope.  Two lines that are parallel always have the same slope. 

 

Plug the value you have for slope (m) and the x and y values you have into the slope intercept format and solve for b (your y intercept)

 

y=mx+b

-1=(-1/7)(3)+b

-1=(-3/7) +b

(-4/7)=b

 

Now you can plug your slope and y intercept into the slope intercept format to get your answer. 

 

y=(-1/7)X+(-4/7)

 

Hope this helps!

 

 

 

 

Answer 2

First, find the slope of your second line.

 

m = (y₂-y_1)/(x2_-x1)

 

m = 4-3  = 1

      -6-1   -7

 

Parallel lines have the same slope. So, now you have to write the equation of a line with a slope of -1/7 and passing through the point (3,-1).

 

y - y₁ = m(x - x₁)

 

y+1 = -1/7(x - 3)

y + 1 = -1 x + 3

              7       7

 

y = -1 x - 4

       7       7