Question

Figure out what the slope and points from the equation are

y + 9 = 2(x + 5)

y - 4 = -3(x - 3)

Answer 1

y + 9 = 2(x + 5)
y + 9 = 2x + 10
-9 -9
y = 2x + 1
slope = 2x
b = 1

y - 4 = -3(x - 3)
y - 4 = -3x + 9
+4 +4
y = -3x + 13
slope = -3x
b = 13

Answer 2

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)