Question

write an equation of the line that passes through the pair of points. (-5,1), (0,-3)

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(-5, 1)\) and \((x_2, y_2)=(0, - 3)\). Then \( m=\frac{-3 - 1}{0-(-5)}=\frac{-4}{5}=-\frac{4}{5} \)

Step2: Use the slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( b \) is the y - intercept. We know that the line passes through \((0,-3)\), so when \( x = 0 \), \( y=-3 \). Substituting \( m =-\frac{4}{5}\) and \( (x,y)=(0,-3) \) into \( y=mx + b \), we get \(-3=-\frac{4}{5}(0)+b\), which simplifies to \( b=-3 \)

Step3: Write the equation

Substitute \( m =-\frac{4}{5}\) and \( b=-3 \) into the slope - intercept form \( y = mx + b \). We get \( y=-\frac{4}{5}x-3 \)

Answer:

\( y =-\frac{4}{5}x - 3 \)