WWTBAM Bored

I was helping the daughter of one of our friends study for her upcoming SAT's and ran into a math problem that stumped me. I thought I knew how to solve it but my answer did not jibe with the choices given. If you can figure this one out please let me know how you did it. Here is the question.

In the xy-plane the line y = ax + 5 is parallel to the line 3x + 8y = 10. What is the value of a?

Sir_Galahad wrote:I was helping the daughter of one of our friends study for her upcoming SAT's and ran into a math problem that stumped me. I thought I knew how to solve it but my answer did not jibe with the choices given. If you can figure this one out please let me know how you did it. Here is the question.

In the xy-plane the line y = ax + 5 is parallel to the line 3x + 8y = 10. What is the value of a?

a = -3/8

Taking the second equation and solve for y:

3x + 8y = 10

8y = 10 - 3x

y = 10/8 - 3/8 x

If the lines are parallel, you don't care about the y-intercept, but the slope (i.e. the factor of x) must be the same, so a = -3/8. QED.

At first glance, I'd say that a = -3/8. The general form of a line is y = mx + b, where m is the slope. Parallel lines have the same slope, so in the second equation, just put it in the form of y = mx + b, and m is the slope, which is -3/8.

it's definitely -3/8

NellyLunatic1980 wrote:it's definitely -3/8

Agreed

Boy, was I going about it the wrong way! I was thinking to solve for either x or y in the second equation and then plug the answer back into the first equation. But, that did not work. I forgot about using the slope. How simple! Thanks.