Given the line y=-5x+12.8, determine the y-intercept

Question

Given the line y=-5x+12.8, determine the y-intercept of the line parallel to the given line that passes through the point (5, 2).

Answer 1

Hi Sandy,

Parallel lines have the same slope.

so the equation of the parallel line would be

y=-5x +b

where b is the y-intercept.

Substitute the values for x and y from given coordinate values (5,2) and solve for b in the above equation.

Hope this helps!

Answer 2

Since you are interested in a line that is parallel to the given line, they must have the same slope (by the definition of parallel lines). We can write the parallel line as y' = -5x + b. Notice the same slope (-5) but the unknown y-intercept (b).

Since we know that the parallel line passes through the point (5, 2), the point is a solution to the equation. We can plug the numbers into the equation and we get

2 = -5(5) + b

2 = -25 + b

27 = b

Since we found that b = 27, we can complete the equation of the parallel line such that

y' = -5x + 27

More importantly, and to answer your question directly, the y-intercept is b = 27 as we calculated above.