Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 5x+5y=10$

We need to isolate $\displaystyle y$ on the left side of the equation. Subtract $\displaystyle 5x$ from both sides of the equation.

$\displaystyle 5x-5x+5y=10-5x$

Simplify.

$\displaystyle 5y=10-5x$

Divide both sides of the equation by $\displaystyle 5$.

$\displaystyle \frac{5y}{5}=\frac{10}{5}-\frac{5x}{5}$

Simplify.

$\displaystyle y=2-x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=-x+2$

In the given equation:

$\displaystyle m=-1$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle -1$.

$\displaystyle y=-x-2$

Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this form, $\displaystyle m$ equals the slope and $\displaystyle b$ represents where the line intersects the y-axis.

Parallel lines have the same slope: $\displaystyle m$.

Only one choice contains tow lines with the same slope.

$\displaystyle y=2x-2$

$\displaystyle y=2x+12$

The slope for both lines in this pair is $\displaystyle m=2$.

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 7y-6x=1$

We need to isolate $\displaystyle y$ on the left side of the equation. Add $\displaystyle 6x$ to both sides of the equation.

$\displaystyle 7y-6x+6x=1+6x$

Simplify.

$\displaystyle 7y=1+6x$

Divide both sides of the equation by $\displaystyle 7$.

$\displaystyle \frac{7y}{7}=\frac{1}{7}+\frac{6x}{7}$

Simplify.

$\displaystyle y=\frac{1}{7}+\frac{6}{7}x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=\frac{6}{7}x+\frac{1}{7}$

In the given equation:

$\displaystyle m=\frac{6}{7}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle \frac{6}{7}$.

$\displaystyle y=\frac{6}{7}x+\frac{1}{2}$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 9x-5y=16$

We need to isolate $\displaystyle y$ on the left side of the equation. Subtract $\displaystyle 9x$ from both sides of the equation.

$\displaystyle 9x-9x-5y=16-9x$

Simplify.

$\displaystyle -5y=16-9x$

Divide both sides of the equation by $\displaystyle -5$.

$\displaystyle \frac{-5y}{-5}=\frac{16}{-5}-\left ( \frac{9x}{-5} \right )$

Simplify. Remember that when a positive number is divided by a negative number, the answer is always negative.

.$\displaystyle y=-\frac{16}{5}-\left ( -\frac{9}{5}x\right )$

Subtracting a negative number is the same as adding a positive number. Rewrite.

$\displaystyle y=-\frac{16}{5}+\frac{9}{5}x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=\frac{9}{5}x-\frac{16}{5}$

In the given equation:

$\displaystyle m=\frac{9}{5}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle \frac{9}{5}$.

$\displaystyle y=\frac{9}{5}x+5$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 2x-y=1$

We need to isolate $\displaystyle y$ on the left side of the equation. Subtract $\displaystyle 2x$ from both sides of the equation.

$\displaystyle 2x-2x-y=1-2x$

Simplify.

$\displaystyle -y=1-2x$

Divide both sides of the equation by $\displaystyle -1$.

$\displaystyle \frac{-y}{-1}=\frac{1}{-1}-\frac{2x}{-1}$

Simplify. Remember that when a positive number is divided by a negative number, the answer is always negative.

$\displaystyle y=-1-\left ( -2x\right )$

Subtracting a negative number is the same as adding a positive number. Rewrite.

$\displaystyle y=-1+2x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=2x-1$

n the given equation:

$\displaystyle m=2$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle 2$.

$\displaystyle y=2x+\pi$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 20y-16x=40$

We need to isolate $\displaystyle y$ on the left side of the equation. Add $\displaystyle 16x$ to both sides of the equation.

$\displaystyle 20y-16x+16x=40+16x$

Simplify.

$\displaystyle 20y=40+16x$

Divide both sides of the equation by $\displaystyle 20$.

$\displaystyle \frac{20y}{20}=\frac{40}{20}+\frac{16x}{20}$

Simplify.

$\displaystyle y=2+\frac{16}{20}x$

Reduce.

$\displaystyle y=2+\frac{4}{5}x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=\frac{4}{5}x+2$

In the given equation:

$\displaystyle m=\frac{4}{5}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle \frac{4}{5}$.

$\displaystyle y=\frac{4}{5}x+\frac{1}{2}$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 7y-14x=16$

We need to isolate $\displaystyle y$ on the left side of the equation. Add $\displaystyle 14x$ to both sides of the equation.

$\displaystyle 7y-14x+14x=16+14x$

Simplify.

$\displaystyle 7y=16+14x$

Divide both sides of the equation by $\displaystyle 7$.

$\displaystyle \frac{7y}{7}=\frac{16}{7}+\frac{14x}{7}$

Simplify.

$\displaystyle y=\frac{16}{7}+2x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=2x+\frac{16}{7}$

In the given equation:

$\displaystyle m=2$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle 2$.

$\displaystyle y=2x-\frac{4}{7}$ 

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

First, put the given line in $\displaystyle y=mx+b$ form.

$\displaystyle 12y-18x=24$

We need to isolate $\displaystyle y$ on the left side of the equation. Add $\displaystyle 18x$ to both sides of the equation.

$\displaystyle 12y-18x+18x=24+18x$

Simplify.

$\displaystyle 12y=24+18x$

Divide both sides of the equation by $\displaystyle 12$.

$\displaystyle \frac{12y}{12}=\frac{24}{12}+\frac{18x}{12}$

Simplify.

$\displaystyle y=2+\frac{18}{12}x$

Reduce.

$\displaystyle y=2+\frac{3}{2}x$

Rearrange terms to match the slope-intercept form.

$\displaystyle y=\frac{3}{2}x+2$

n the given equation:

$\displaystyle m=\frac{3}{2}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle \frac{3}{2}$.

$\displaystyle y=\frac{3}{2}x-8$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=\frac{1}{2}$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle \frac{1}{2}$.

$\displaystyle y=\frac{1}{2}x+\frac{17}{2}$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=6$

Parallel lines share the same slope.

Only one of the choices has a slope of $\displaystyle 6$.

$\displaystyle y=6x-14$