Geometry - How to find the slope of a line

What is the slope of the line that passes through the points and ?

Explanation

The slope of a line is sometimes referred to as "rise over run." This is because the formula for slope is the change in y-value (rise) divided by the change in x-value (run). Therefore, if you are given two points, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , the slope of their line can be found using the following formula: $slope=(y_{1}-y_{2})/(x_{1}-x_{2})$

This gives us .

Give the slope of the line of the equation

$\textup{The slope is undefined}$

$\frac{1}{8}$

Explanation

If we divide both sides by 8, as follows:

$\frac{8y}{8} = \frac{1}{8}$

$y = \frac{1}{8}$

we see that the equation is equivalent to one of the form . This is a horizontal line, and its slope is 0.

Give the slope of the line of the equation $- \frac{2}{3}x = 4$ .

$\textup{The slope is undefined}$

$- \frac{2}{3}$

$- \frac{3}{2}$

Explanation

If we multiply both sides of the equation by $-\frac{3}{2}$ , as follows:

$- \frac{2}{3}x = 4$

$- \frac{3}{2} \cdot \left (- \frac{2}{3}x \right )=- \frac{3}{2} \cdot 4$

we see that the equation is equivalent to one of the form . This is a vertical line, which has undefined slope.

A line crosses the x-axis at and the y-axis at . What is the slope of this line?

$m=\frac{1}{3}$

$m=-\frac{1}{3}$

None of these.

Explanation

Given the points,

$\(x_1,y_1)=(0,6) \(x_2,y_2)=(6,8)$ .

We compute slope (m) as follows:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{6-0}=\mathbf{\frac{1}{3}}$

What is the slope of a line with an -intercept is and another -intercept of ?

$\infty$

Explanation

The -intercept is the value when .

Therefore, since the two -intercepts are and , the points are and .

Write the slope formula, plug in the values, and solve.

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{0-0}{6-4}= \frac{0}{2} =0$

The slope is zero.

Find the slope of the line that passes through the points:

and

$-\frac{9}{7}$

$-\frac{8}{7}$

$-\frac{10}{7}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{-16-2}{14-0}$

Simplify.

$\text{Slope}=\frac{-18}{14}$

Solve.

$\text{Slope}=-\frac{9}{7}$

Find the slope of the line that passes through the points:

and

$-\frac{1}{2}$

$\frac{7}{8}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{-20-4}{-10-2}$

Simplify.

$\text{Slope}=\frac{-24}{-12}$

Solve.

$\text{Slope}=2$

Find the slope of the line that passes through the points:

and

$\frac{4}{7}$

$\frac{3}{7}$

$-\frac{2}{7}$

$\frac{5}{7}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{1-5}{-3-4}$

Simplify.

$\text{Slope}=\frac{-4}{-7}$

Solve.

$\text{Slope}=\frac{4}{7}$

Find the slope of the line that passes through the points:

and

$\frac{3}{4}$

$\frac{1}{2}$

$-\frac{1}{4}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{20-14}{100-92}$

Simplify.

$\text{Slope}=\frac{6}{8}$

Solve.

$\text{Slope}=\frac{3}{4}$

Find the slope of the line that passes through the points:

and

$\frac{13}{22}$

$\frac{1}{2}$

$-\frac{7}{11}$

$\frac{5}{11}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{12-(-14)}{34-(-10)}$

Simplify.

$\text{Slope}=\frac{26}{44}$

Solve.

$\text{Slope}=\frac{13}{22}$

How to find the slope of a line

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