Answer:
y + 9 = 2(x + 5): slope is 2
y - 4 = -3(x - 3): slope is -3
(12/5, 29/5)
Explanation:
y + 9 = 2(x + 5)
y + 9 - 9 = 2(x + 5) - 9 ==> subtract both sides by 9 to isolate y
y = 2(x + 5) - 9 ==> simplify
y = 2x + 2*5 - 9 ==> distribute x and 5 by multiplying them by 2
y = 2x + 10 - 9
y = 2x + 1 ==> slope is 2
y - 4 = -3(x - 3)
y - 4 + 4 = -3(x - 3) + 4 ==> add both sides by 4 to isolate y
y = -3(x - 3) + 4
y = -3x - 3(-3) + 4 ==> multiply x and -3 by -3 by distributive property
y = -3x - (-9) + 4
y = -3x + 9 + 4 ==> simplify
y = -3x + 13 ==> slope is -3
Since y = -3x + 13 and y = 2x + 1:
2x + 1 = -3x + 13 ==> solve for x
2x + 3x + 1 = -3x + 3x + 13
5x + 1 = 13
5x + 1 - 1 = 13 - 1
5x = 12
x = 12/5
y = 2x + 1
y = 2(12/5) + 1 ==> plug in 12/5 for x
y = 24/5 + 1 ==> solve for y
y = 24/5 + 5/5
y = (24+5)/5 ==> y = 29/5 ==> (x, y) = (12/5, 29/5)