Q6. - Algebra 1

Question

Graph each equation.

 $\mathbf{2}\mathit{x}\mathbf{+}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{6}$

Step-by-Step Solution

Answer

The graph of the equation is:

y = m x + b 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 $2x+y=-6$ in slope-intercept form.

 The equation of the straight line is:

$\begin{array}{l}2x+y=-6\\ 2x+y-2x=-6-2x\text{ Subtract 2}x\text{ from both sides}\\ y=-2x-6\end{array}$

The slope is $m=-2$ and the $y$-intercept is $(0,-6)$.

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept $(0,-6)$. The slope is $\frac{\text{rise}}{\text{run}}=-\frac{2}{1}$. From $(0,-6)$, move down 2 unit and right 1 unit. Plot the point. Draw the line through the two points.