Question

find an equation for the line with the given properties. express your answer using either the general form or the slope - intercept form of the equation of a line. x - intercept = 5; y - intercept = - 2 the equation is (type an equation. simplify your answer.)

Explanation:

Step1: Identify Intercept Points

The x - intercept is 5, so the point is \((5, 0)\). The y - intercept is - 2, so the point is \((0, - 2)\).

Step2: Calculate the Slope

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((5,0)\) and \((0, - 2)\), we have \(m=\frac{-2 - 0}{0 - 5}=\frac{-2}{-5}=\frac{2}{5}\).

Step3: Use Slope - Intercept Form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know \(m = \frac{2}{5}\) and \(b=-2\), so the equation is \(y=\frac{2}{5}x-2\). We can also convert it to general form: \(2x - 5y=10\) (by multiplying both sides of \(y=\frac{2}{5}x - 2\) by 5 to get \(5y = 2x-10\), then rearranging to \(2x-5y = 10\)).

Answer:

\(y=\frac{2}{5}x - 2\) (or \(2x-5y = 10\))