Question

what is the slope of the line given by the following equation:
$x = 3$
\\(\bigcirc\\) 3
\\(\bigcirc\\) 0
\\(\bigcirc\\) undefined
question 17 (4 points)
write the equation of the line with slope $m = 4$ that passes through the point $(-3, 5)$
\\(\bigcirc\\) $y - 5 = 4(x + 3)$
\\(\bigcirc\\) $y + 5 = 4(x - 3)$
\\(\bigcirc\\) $y - 3 = 4(x + 5)$
\\(\bigcirc\\) $y + 3 = 4(x - 5)$

Explanation:

Step1: Analyze line $x=3$

The line $x=3$ is vertical, with all points having $x=3$. Slope is $\frac{\Delta y}{\Delta x}$, and $\Delta x=0$. Division by 0 is undefined.

Step2: Use point-slope form for line

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=4$, $x_1=-3$, $y_1=5$:
$y-5=4(x-(-3))$
Simplify to $y-5=4(x+3)$

Answer:

1. undefined
2. $y - 5 = 4(x + 3)$