# Algebra 1 : How to find slope of a line

## Example Questions

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### Example Question #1 : How To Find Slope Of A Line

What is the slope of the equation 4x + 3y = 7?

4/3

3/4

–4/3

–3/4

–7/3

–4/3

Explanation:

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

Isolate the y term: 3y = 7 – 4x

Divide by 3: y = 7/3 – 4/3 * x

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

### Example Question #2 : How To Find Slope Of A Line

Find the slope of the line through the points (6,2) and (3,4).

Explanation:

The equation for slope is . You plug in the coordinates from the points given you, and get , giving you . Note that it does not matter which point you use as point 1 and point 2, as long as you are consistent.

(6,2) = (x1,y1)

(3,4) = (x2,y2)

### Example Question #2 : How To Find Slope Of A Line

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

1/4

2

–1/4

1/2

–2

1/2

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.

### Example Question #3 : How To Find Slope Of A Line

What is the slope of the line containing the points (7,12) and (91,32).

Explanation:

To find the slope of a line you must first assign variables to each point. It does not matter which points get which variables as long as you keep the  and  and  and  consistent when you plug them into the equation.

Then we plug in the variables to this equation where  represents the slope.

Then we plug in our points for and the example looks like

Then we perform the necessary subtraction and division to find an answer of

Explanation:

### Example Question #6 : How To Find Slope Of A Line

Which of the following is an example of an equation written in slope-intercept form?

Explanation:

Slope intercept form is , where  is the slope and  is the y-intercept.

is the correct answer. The line has a slope of  and a y-intercept equal to .

### Example Question #5 : How To Find Slope Of A Line

If (1,2) and (4,6) are on the same line, what is the slope of the line?

Explanation:

### Example Question #6 : How To Find Slope Of A Line

The equation of a line is:

What is the slope of the line?

Explanation:

Solve the equation for

where  is the slope of the line:

### Example Question #7 : How To Find Slope Of A Line

A line passes through the points  and .  What is its slope?

-

Explanation:

The slope is the rise over the run.  The line drops in -coordinates by 13 while gaining 5 in the -coordinates.

### Example Question #10 : How To Find Slope Of A Line

What is the slope of the line ?