Question

1. points: (4, -5) and (-8, -14)

equation: _______________

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1 = 4,y_1=-5,x_2=-8,y_2=-14 \). So \( m=\frac{-14 - (-5)}{-8 - 4}=\frac{-14 + 5}{-12}=\frac{-9}{-12}=\frac{3}{4} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((4,-5)\) and \( m = \frac{3}{4} \), we have \( y-(-5)=\frac{3}{4}(x - 4) \).
Simplify this equation: \( y + 5=\frac{3}{4}x-3 \). Then \( y=\frac{3}{4}x-3 - 5 \), so \( y=\frac{3}{4}x-8 \). To convert to standard form (or keep in slope - intercept), we can also write it as \( 3x-4y = 32 \) (by multiplying both sides by 4: \( 4y+20 = 3x - 12\), then \( 3x-4y=32 \)).

Answer:

The equation of the line is \( y=\frac{3}{4}x - 8 \) (or \( 3x-4y = 32 \))