Question

write an equation of the line. the graph shows a line passing through the points (-5, 3) and (0, -7).

Explanation:

Step1: Find the slope (m)

We use the two points \((-5, 3)\) and \((0, -7)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{-7 - 3}{0 - (-5)}=\frac{-10}{5}=-2\)

Step2: Identify the y - intercept (b)

The y - intercept is the value of y when \(x = 0\). From the point \((0, -7)\), we see that \(b=-7\).

Step3: Write the equation in slope - intercept form (\(y=mx + b\))

Substitute \(m=-2\) and \(b = - 7\) into the formula: \(y=-2x-7\)

Answer:

\(y = - 2x-7\)