Question

Find an equation of the line that

a. has the same y-intercept as the line y+7x+3=0 and

b. Is parallel to the line -11x-12y=-7

Write your answer in the form y=mx+b

Answer 1

y = (-11/12)x - 3

Explanation:

Recall that for a linear equation in the form y = mx + b,

m = slope and b = y-intercept.

hence to satisfy parts (a) and (b) of the questions, we need to extract the y-intercept from the equation in part (a) and the slope from part (b)

For part (a)

given: y+7x+3=0 (rearrange this to get slope-intercept form)

y+7x+3=0 (subtract 3 from both sides)

y + 7x = -3 (subtract 7x from both sides)

y = -7x - 3

we can see that the y-intercept is -3.

For part (b)

given: -11x -12y=-7 (rearrange this to get slope-intercept form)

-11x -12y=-7 (add 11x toboth sides)

-12y = 11x - 7 (divide both sides by -12)

y = (-11/12) - (7/12)

we can see that the slope is (-11/12).

combining the y-intercept from part (a) and the slope from part (b) into the general equation given in the first line above,

y = (-11/12)x - 3 (answer)