Forms of linear equations: summary

1. A. $-\frac{7}{2}$

We can determine the slope of the graph by bringing the equation to slope-intercept form. So let’s solve the equation for $y$:

$\begin{aligned}7 x+2 y &=5 \\2 y &=5-7 x \\y &=\frac{5}{2}-\frac{7}{2} x\end{aligned}$

Now we have the equation in slope-intercept form: $y=m \cdot x+b$. In this form, the slope is simply the coefficient of $x$, meaning the value of $m$.

The slope is $-\frac{7}{2}$.

2. C. $\frac{2}{3}$

We can determine the slope of the graph by bringing the equation to slope-intercept form. So let’s solve the equation for $y$:

$\begin{array}{r} 3(y-1)=2 x+2 \\ 3 y-3=2 x+2 \\ 3 y=2 x+5 \\ y=\frac{2}{3} x+\frac{5}{3} \end{array}$

Now we have the equation in slope-intercept form: $y=m \cdot x+b$. In this form, the slope is simply the coefficient of $x$, meaning the value of $m$.

The slope is $\frac{2}{3}$

3. B. $\frac{4}{3}$

We can determine the slope of the graph by bringing the equation to slope-intercept form. So let’s solve the equation for $y$:

$\begin{aligned} &8 x-6 y=1 \\ &8 x-1=6 y \\ &\frac{8}{6} x-\frac{1}{6}=y \\ &\frac{4}{3} x-\frac{1}{6}=y \end{aligned}$

Now we have the equation in slope-intercept form: $y=m \cdot x+b$. In this form, the slope is simply the coefficient of $x$, meaning the value of $m$.

The slope is $\frac{4}{3}$

4. C. $3$

The equation is given in point-slope form, $y-y_{1}=m\left(x-x_{1}\right)$.

In this form, $m$ is the slope.

The slope is $3$.