Question

graph the line that passes through the points (0, 4) and (-6, 9) and determine the equation of the line.

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(0, 4)\) and \((x_2, y_2)=(-6, 0)\). Then \(m=\frac{0 - 4}{-6 - 0}=\frac{-4}{-6}=\frac{2}{3}\).

Step2: Use 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 \((0, 4)\), so when \(x = 0\), \(y = 4\). Substituting \(x = 0\), \(y = 4\) and \(m=\frac{2}{3}\) into \(y=mx + b\), we get \(4=\frac{2}{3}(0)+b\), so \(b = 4\).

Step3: Write the equation

Substitute \(m=\frac{2}{3}\) and \(b = 4\) into \(y=mx + b\). The equation of the line is \(y=\frac{2}{3}x + 4\).

Answer:

\(y=\frac{2}{3}x + 4\)