Question

1. through: (5, 0), slope = -\frac{1}{2}
2. through: (5, 4), slope = \frac{1}{5}
3. through: (-1, -5), slope = 8
4. through: (2, -2), slope = -\frac{7}{2}

Explanation:

Problem 12:

Step1: Use point - slope form $y - y_1=m(x - x_1)$

Given point $(5,0)$ and slope $m =-\frac{1}{2}$, substitute into the formula: $y - 0=-\frac{1}{2}(x - 5)$

Step2: Simplify the equation

$y=-\frac{1}{2}x+\frac{5}{2}$

Step1: Use point - slope form $y - y_1=m(x - x_1)$

Given point $(5,4)$ and slope $m=\frac{1}{5}$, substitute into the formula: $y - 4=\frac{1}{5}(x - 5)$

Step2: Simplify the equation

$y-4=\frac{1}{5}x - 1$, then $y=\frac{1}{5}x+3$

Step1: Use point - slope form $y - y_1=m(x - x_1)$

Given point $(-1,-5)$ and slope $m = 8$, substitute into the formula: $y-(-5)=8(x - (-1))$

Step2: Simplify the equation

$y + 5=8(x + 1)$, $y+5 = 8x+8$, then $y=8x + 3$

Answer:

$y =-\frac{1}{2}x+\frac{5}{2}$

Problem 14: