Question

Graph each equation.

$\mathbf{-}\mathbf{4}\mathit{x}\mathbf{+}\mathit{y}\mathbf{=}\mathbf{2}$

Short answer

The graph of the equation is:

Step-by-step solution

Step 1. State the concept of slope-intercept of an equation.

The slope-intercept form of a linear equation is , where $m$is the slope and $b$is the$y$-intercept.

Step 2. Write equation of a line in slope-intercept form.

Rewrite the equation$-4x+y=2$in slope-intercept form.

The equation of the straight line is:

localid="1647497910718" $\begin{array}{l}-4x+y=2\\ -4x+y+4x=2+4x\text{Add4}x\text{bothsides}\\ y=4x+2\end{array}$

The slope islocalid="1647426666843" $m=4$and the localid="1647426662825" $y$-intercept is $(0,2)$.

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept$(0,2)$. The slope is $\frac{\text{rise}}{\text{run}}=\frac{4}{1}$. From, move up 4 unit and right 1 unit. Plot the point. Draw the line through the two points.