Q19. - Algebra 1

Question

Write each equation in slope-intercept form.

$y-3=4\left(x+3\right)$

Step-by-Step Solution

Answer

The equation in slope-intercept form is $\mathit{y}\mathbf{=}\mathbf{4}\mathit{x}\mathbf{+}\mathbf{15}$. 

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

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

Step 2. Simplify the equation.

In order to simplify $y-3=4\left(x+3\right)$, apply the distributive property on the right side.

$$\begin{gathered} y-3=4\left(x+3\right) \\ y-3=4x+4\times 3 \\ y-3=4x+12 \end{gathered}$$

Step 3. Write the equation in slope-intercept form.

Further, simplify the equation so as to rewrite the equation in the needed form of $y=mx+b$.

$$\begin{gathered} y-3=4x+12 \\ y-3+3=4x+12+3\text{ Add 3 to each side} \\ y=4x+15 \end{gathered}$$

Thus, the equation in slope-intercept form is $y=4x+15$.