Q20. - Algebra 1

Question

Write each equation in slope-intercept form.

$y+1=\frac{1}{2}\left(x-8\right)$

Step-by-Step Solution

Answer

The equation in slope-intercept form is $\mathit{x}\mathbf{-}\mathbf{2}\mathit{y}\mathbf{=}\mathbf{10}$. 

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 $y+1=\frac{1}{2}\left(x-8\right)$, first multiply both sides by 2 and then apply the distributive property.

$$\begin{gathered} y+1=\frac{1}{2}\left(x-8\right) \\ 2\times \left(y+1\right)=2\times \frac{1}{2}\left(x-8\right) \\ 2y+2=x-8 \end{gathered}$$

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

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

  $$\begin{gathered} 2y+2=x-8 \\ 2y+2-2=x-8-2\text{ Subtract 2 from each side} \\ 2y=x-10\text{ Subtract }x\text{ from both sides} \\ \left(-1\right)\times \left(2y-x\right)=\left(-1\right)\times \left(-10\right)\text{ Multiply both sides by -1} \\ x-2y=10 \end{gathered}$$ 

Thus, the equation in slope-intercept form is $x-2y=10$.