Q. 53 - Precalculus Enhanced with Graphing Utilities

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, whichever you prefer.

x- intercept is 2 and y-intercept is $-1$

Step-by-Step Solution

Answer

The equation of line is $y=\frac{1}{2}x-1$

Step 1. Given Information

The given x-intercept and y-intercept are $2 and -1$respectively.

Step 2. Calculation

Since x-intercept is 2 and y-intercept is $-1$, one point on the line will be $(2,0)$ and the other point will be $(0,-1)$

Use the points to find the slope of line.

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{0-(-1)}{2-0} \\ =\frac{1}{2} \end{gathered}$$

Use the slope intercept form of an equation and substitute the given values in it.

$$\begin{gathered} y=mx+b \\ y=\frac{1}{2}x-1 \end{gathered}$$