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 \(3\).