Find a formula for the line parallel to the line y=110-8x and containing the point (7,56)

Question

Can someone show me step by step on how to solve this problem?

Answer 1

Hi Adriana,

 

The general equation is y = mx + b where m is the slope and b is the y intercept (the place where the line hits the y axis).

 

So rewrite the equation by switching the locations of the two terms on the right--> y = -8x + 110

 

So the slope is -8.  Parallel lines have the same slope.  We are given the x (7) and the y (56) so we have all we nee to solve for the y intercept of the new line:

 

56 = (-8)(7) + b

 

56 = -56 + b

 

b = 112

 

So the equation of the parallel line is y = -8x + 112

 

Dan

Answer 2

The line y= 110 - 8x is properly written y = -8x + 110 in slope intercept form.  The slope of the line is the coefficient of the x term, -8.  Any line parallel to the original line will have the same slope and a different y-intercept.

 

simply take the generic slope-intercept equation and substitute the desired values for x and y and solve for the y-intercept (b).

 

y = mx + b

(56) = (-8)(7) + b

56 = -56 + b

112 = b

 

so y = -8x + 112 

is parallel to y = -8x +110

and goes through the point (7,56)