Question

1) Identify the correct slope and y-intercept of the equation y - 4x = -3
A)slope = -1; y-intercept = (0, -3)
B) slope = -1 over 4 ; y-intercept = (0, 3)
C) slope = 4; y-intercept = (0, -3)
D) slope = 4; y-intercept = (0, 3)

2)
Choose the slope-intercept equation of the line that passes through the point (6, -6) and is perpendicular to y = 3x - 6.
A) y = 1 over 3x - 8
B) y = -3x + 12
C) y = 3x - 24
D) y = -1 over 3x - 4

just need help with these two then I can do the rest on my own.

Answer 1

# 1


Solve for y:


y - 4x = -3


y - 4x+4x = -3+4x


y = 4x-3


The equation is now in slope intercept form y = mx+b where m is the slope and (0, b) is the y-intercept


We can see that m = 4 and b = -3


So the slope is 4 and the y-intercept is (0, -3)


So the answer is choice C

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# 2


Anything perpendicular to y = 3x - 6 will have a slope of -1/3.


Simply flip the original slope 3/1 to get 1/3 and change the sign to get -1/3


So use this along with the point (6,-6) with y = mx+b to find the perpendicular equation


You'll be plugging in

m = -1/3
x = 6
y = -6


\[\Large y = mx+b\]


\[\Large -6 = \left(\frac{-1}{3}\right)\left(6\right)+b\]


\[\Large -6 = \frac{-6}{3}+b\]


\[\Large -6 = -2+b\]


\[\Large -6+2 = b\]


\[\Large -4 = b\]


\[\Large b = -4\]


So the equation of the perpendicular line is \[\Large y = -\frac{1}{3}x-4\]


So the answer is choice D

Answer 2

Thank you, that helped me a lot, made more sense!

Answer 3

Glad to be of help.

Answer 4

and I'm glad things are starting to click for you.