A line has an equation of 2x+5y=7. Another line passes through (3,6) and (k,9). What is k if the lines are...?

Question

...parallel?

Answer 1

Slope of 1st line is -2/5 which is also slope of 2nd line since they are ||.
Thus (9-6)/(k-3) = -2/5
3*5 = -2k+6
9 = -2k
k = -4.5

Answer 2

5y=-2x+7, y=(-2/5)x+(7/5), so the slope of this line is (-2/5), If the lines are to be parallel, they have to have the same slope.

-2/5 is the slope of the first line: To find k:
(-2/5)=(9-6)/(k-3), since the slope of a line is the difference between two poitnts that is: Now you just cross multiply and solve for k:
15=-2k+6, k=-4.5

Answer 3

Slope of first line:
2x + 5y = 7
5y = -2x + 7
y = (-2/5)y + (7/5)

slope = -2/5

Slope of the other line must be the same for them to be parallel.

So, slope of line through (3, 6) and (k, 9)

(9 - 6) / (k - 3) = -2/5
3 / (k - 3) = -2 / 5
5*3 = -2(k - 3)
15 = -2k + 6
11 = -2k
-11/2 = k