Questions: Graph the linear equation by finding and plotting its intercepts. -3=2x-y Use the graphing tool to graph the linear equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Graph the linear equation by finding and plotting its intercepts.
-3=2x-y

Use the graphing tool to graph the linear equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Transcript text: Graph the linear equation by finding and plotting its intercepts. \[ -3=2 x-y \] Use the graphing tool to graph the linear equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Solution

Solution Steps

Step 1: Rewrite the Equation in Slope-Intercept Form

The given equation is \(-3 = 2x - y\). To rewrite it in slope-intercept form (\(y = mx + b\)), solve for \(y\): \[ -3 = 2x - y \implies y = 2x + 3 \]

Step 2: Find the Y-Intercept

The y-intercept is the value of \(y\) when \(x = 0\). From the equation \(y = 2x + 3\): \[ y = 2(0) + 3 = 3 \] So, the y-intercept is \((0, 3)\).

Step 3: Find the X-Intercept

The x-intercept is the value of \(x\) when \(y = 0\). Set \(y = 0\) in the equation \(y = 2x + 3\): \[ 0 = 2x + 3 \implies 2x = -3 \implies x = -\frac{3}{2} \] So, the x-intercept is \(\left(-\frac{3}{2}, 0\right)\).