asked 172k views
1 vote
HELP PLS xx

A and B are the points (a, −5) and (2, -8) respectively. AB is parallel to the line with equation 5y-3x =10. Determine the value of a.

1 Answer

2 votes

Explanation:

the parallel line is defined as

5y - 3x = 10

let's bring it into a slope-intercept form to see the slope directly :

y = mx + b

"m" being the slope, "b" being the y-intercept (the y-value of the point where the line crosses the y-axis; the x- coordinate of any point on the y-axis is 0).

so,

5y - 3x = 10

5y = 3x + 10

y = ⅗x + 10/5 = ⅗x + 2

the slope of that line is therefore ⅗.

remember, the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

that means for our given 2 points (as parallel lines must have the same slope), as I see in a line AB B as the endpoint (but we could also do the differences the other way around) :

(-8 - -5)/(2 - a) = 3/5

(-8 + 5)/(2 - a) = 3/5

-3/(2 - a) = 3/5

the slope has to be positive, because 3/5 is positive.

that means, as the numerator is negative (-3), the denominator has to be negative too (as -/- = +).

therefore,

2 - a = -5

2 = a - 5

a = 2 + 5 = 7

the point is therefore (7, -5).

answered
User Koehn
by
7.5k points

No related questions found

Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.