Question

1. points: (-5, -3) and (-15, -7)

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, \( x_1=-5,y_1 = - 3,x_2=-15,y_2=-7 \). So \( m=\frac{-7-(-3)}{-15-(-5)}=\frac{-7 + 3}{-15 + 5}=\frac{-4}{-10}=\frac{2}{5} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-5,-3)\) and \( m = \frac{2}{5} \), we have \( y-(-3)=\frac{2}{5}(x - (-5)) \), which simplifies to \( y + 3=\frac{2}{5}(x + 5) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y+3=\frac{2}{5}x+2 \). Subtract 3 from both sides: \( y=\frac{2}{5}x+2 - 3=\frac{2}{5}x-1 \). We can also write it in standard form \( 2x-5y = 5 \) (by multiplying both sides of \( y=\frac{2}{5}x - 1\) by 5 to get \( 5y=2x - 5\), then rearranging to \( 2x-5y = 5\)).

Answer:

The equation of the line is \( y=\frac{2}{5}x - 1 \) (or \( 2x-5y = 5 \))