To find the equation of a line passing through these points we must find a line with that same slope. Start by finding the slope between the two points and then use the point slope equation to find the equation of the line.

slope:

\(\displaystyle m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0--5}{5-0}=1\)

Now use the point slope equation:

\(\displaystyle y-y_{1}=m(x-x_{1})\rightarrow y-(-5)=1(x-0)\rightarrow \mathbf{y=x-5}\)

*make sure you use the SAME coordinate pair when substituting x and y into the point slope equation.

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{5-12}{-2-3}=\frac{7}{5}\)

Next, find the y-intercept of the line by plugging in \(\displaystyle 1\) of the points into the semi-completed formula.

\(\displaystyle y=\frac{7}{5}x+b\)

Plugging in \(\displaystyle (3, 12)\) yields the following:

\(\displaystyle 12=\frac{7}{5}(3)+b\)

Solve for \(\displaystyle b\).

\(\displaystyle b+\frac{21}{5}=12\)

\(\displaystyle b=\frac{39}{5}\)

The equation of the line is then \(\displaystyle y=\frac{7}{5}x+\frac{39}{5}\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{8-7}{12-(-10)}=\frac{1}{22}\)

Next, find the y-intercept of the line by plugging in \(\displaystyle 1\) of the points into the semi-completed formula.

\(\displaystyle y=\frac{1}{22}x+b\)

Plugging in \(\displaystyle (12, 8)\) yields the following:

\(\displaystyle 8=\frac{1}{22}(12)+b\)

Solve for \(\displaystyle b\).

\(\displaystyle b+\frac{6}{11}=8\)

\(\displaystyle b=\frac{82}{11}\)

The equation of the line is then \(\displaystyle y=\frac{1}{22}x+\frac{82}{11}\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{10-2}{16-15}=8\)

Next, find the y-intercept of the line by plugging in \(\displaystyle 1\) of the points into the semi-completed formula.

\(\displaystyle y=8x+b\)

Plugging in \(\displaystyle (16, 10)\) yields the following:

\(\displaystyle 10=8(16)+b\)

Solve for \(\displaystyle b\).

\(\displaystyle b+128=10\)

\(\displaystyle b=-118\)

The equation of the line is then \(\displaystyle y=8x-118\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{8-(-5)}{-4-(-3)}=-13\)

Next, find the y-intercept of the line by plugging in \(\displaystyle 1\) of the points into the semi-completed formula.

\(\displaystyle y=-13x+b\)

Plugging in \(\displaystyle (-3, -5)\) yields the following:

\(\displaystyle -5=-13(-3)+b\)

Solve for \(\displaystyle b\).

\(\displaystyle b+39=-5\)

\(\displaystyle b=-44\)

The equation of the line is then \(\displaystyle y=-13x-44\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{0-16}{12-0}=-\frac{4}{3}\)

The y-intercept is \(\displaystyle 16\) since that is given as one of the points on the line.

The line must have the equation \(\displaystyle y=-\frac{4}{3}x+16\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{18-(-36)}{20-(-40)}=\frac{9}{10}\)

Next, find the y-intercept of the line by plugging in \(\displaystyle 1\) of the points into the semi-completed formula.

\(\displaystyle y=\frac{9}{10}x+b\)

Plugging in \(\displaystyle (20, 18)\) yields the following:

\(\displaystyle 18=\frac{9}{10}(20)+b\)

Solve for \(\displaystyle b\).

\(\displaystyle b+18=18\)

\(\displaystyle b=0\)

The equation of the line is then \(\displaystyle y=\frac{9}{10}x\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{20-(-10)}{15-5}=3\)

Next, find the y-intercept of the line by plugging in \(\displaystyle 1\) of the points into the semi-completed formula.

\(\displaystyle y=3x+b\)

Plugging in \(\displaystyle (5, -10)\) yields the following:

\(\displaystyle -10=3(5)+b\)

Solve for \(\displaystyle b\).

\(\displaystyle b+15=-10\)

\(\displaystyle b=-25\)

The equation of the line is then \(\displaystyle y=3x-25\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{10-2}{11-11}=\text{Undefined}\)

Since the slope of the line is undefined, this must be just a vertical line with the equation \(\displaystyle x=11\).

Recall that the slope-intercept form of a line:

\(\displaystyle y=mx+b\),

where \(\displaystyle m=\text{slope}\) and \(\displaystyle b=\text{y-intercept}\).

First, find the slope of the line by using the following formula:

\(\displaystyle \text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle \text{Slope}=\frac{7-7}{5-(-8)}=0\)

Since the slope is \(\displaystyle 0\), the line is a horizontal line with the equation \(\displaystyle y=7\).