Algebra - How to find slope of a line

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

and

$\frac{1}{7}$

Explanation

The slope of a line can be found using the formula:

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

Remember that points are written in the format:

For the given points,

$\text{Slope}=\frac{5-(-2)}{0-(-1)}$

Remember that subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{5+2}{0+1}$

$\text{Slope}=\frac{7}{1}$

Simplify.

$\text{Slope}=7$

Find the slope of the following line:

$\frac{-2}{3}$

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{-3}{2}$

Explanation

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

$y=\frac{-2}{3}x+\frac{5}{3}$

The slope is the number in front of the "x" which in this case is -2/3

Find the slope of the coordinates.

$\frac{7}{2}$

$\frac{2}{7}$

$-\frac{1}{2}$

$-\frac{7}{2}$

Explanation

To find slope, it is differences of the -coordinates divided by the differences of the coordinates.

$\frac{3-(-4)}{2-0}=\frac{7}{2}$

What is the slope of the equation 4_x_ + 3_y_ = 7?

–4/3

4/3

3/4

–3/4

–7/3

Explanation

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4_x_ + 3_y_ = 7.

Isolate the y term: 3_y_ = 7 – 4_x_

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

Given the line 4y = 2x + 1, what is the slope of this line?

1/2

1/4

–1/4

–2

Explanation

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

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

and

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{1}{3}$

Explanation

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

For this line,

$\text{Slope}=\frac{7-2}{5-(-1)}$

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

$\text{Slope}=\frac{7-2}{5+1}$

$\text{Slope}=\frac{5}{6}$

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

and

$-\frac{1}{3}$

$\frac{1}{3}$

$-\frac{13}{3}$

Explanation

Use the following formula to find the slope:

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

Remember that points are written in the following format:

Substitute using the given points:

$\text{Slope}=\frac{2-6}{7-(-5)}$

Remember that subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{2-6}{7+5}$

Simplify.

$\text{Slope}=-\frac{4}{12}$

Reduce.

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

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

Undefined

Explanation

We have been given a set of coordinate points in order to find the slope of the line that runs through it.

We can use the equation:

$\frac{y_2-y_1}{x_2-x_1}= \frac{9-1}{9-9}=\frac{8}0$

Since the resulting denominator is 0, it is determined that the slope is a vertical line (since there was no horizontal movement) with an undefined slope or 'no slope'.

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

and

$\text{Undefined}$

Explanation

Use the following formula to find the slope:

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

Remember that points are written in the following format:

Substitute using the given points:

$\text{Slope}=\frac{7-1}{1-1}$

Simplify.

$\text{Slope}=\frac{6}{0}$

Since you cannot divide by , the slope of this vertical line is undefined.

Find the slope between the following coordinate points:

and

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{6}$

Explanation

In order to find the slope, we must find the difference in coordinates and divide this number by the difference between the coordinates.

$\text{Slope}=\frac{5-3}{4-2}=\frac{2}{2}=1$

How to find slope of a line

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