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Inequalities & Graphing

Slope-Intercept Form

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

✨ y = mx + b is one of the most useful equations in all of algebra — once you know it, graphing lines is a breeze!

Visualize It

y = mx + b: slope m, y-intercept b

y=2x+1y=−x+4xy-8-8-6-6-4-4-2-2224466880b=1b=4

Watch & Learn

Watch a clear, friendly video explanation of Slope-Intercept Form:

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Worked Examples

Follow along with these step-by-step examples. Take your time — there's no rush!

1Example 1

Problem

Identify the slope and y-intercept of y = 3x − 5

Step-by-Step Solution

1

Compare to y = mx + b.

2

m = 3 (slope)

3

b = −5 (y-intercept, the line crosses the y-axis at −5)

Answer

Slope = 3, y-intercept = −5

y = 3x − 5

y=3x−5xy-8-8-6-6-4-4-2-2224466880(0,−5)
2Example 2

Problem

Write the equation of a line with slope 2 and y-intercept 4

Step-by-Step Solution

1

Use y = mx + b.

2

Substitute m = 2 and b = 4.

3

y = 2x + 4

Answer

y = 2x + 4

y = 2x + 4

y=2x+4xy-8-8-6-6-4-4-2-2224466880(0,4)
3Example 3

Problem

Graph y = −x + 3

Step-by-Step Solution

1

y-intercept: b = 3, so start at (0, 3).

2

Slope: m = −1, so go down 1 and right 1 to get next point (1, 2).

3

Connect the points with a straight line.

Answer

Start at (0,3), slope goes down-right

y = −x + 3

y=−x+3xy-8-8-6-6-4-4-2-2224466880(0,3)(1,2)
4Example 4

Problem

What is the y-intercept of y = −4x + 9?

Step-by-Step Solution

1

Compare to y = mx + b.

2

m = −4 (slope), b = 9 (y-intercept).

3

The line crosses the y-axis at (0, 9).

Answer

y-intercept = 9, at point (0, 9)

y = −4x + 9

y=−4x+9xy-8-8-6-6-4-4-2-2224466880(0,9)
5Example 5

Problem

A line passes through (0, −2) with slope 3. Write its equation.

Step-by-Step Solution

1

We know b = −2 (y-intercept) and m = 3.

2

Substitute into y = mx + b.

3

y = 3x − 2

Answer

y = 3x − 2

y = 3x − 2

y=3x−2xy-8-8-6-6-4-4-2-2224466880(0,−2)

Your Turn — Practice Problems

Try all 5 problems on your own first. Write out your work — that's how it sticks!

💡 Tip: Don't peek at the answers until you've genuinely tried each one.

1

What is the slope of y = 5x + 2?

2

What is the y-intercept of y = −3x + 7?

3

Write the equation with slope −2 and y-intercept 6

4

Look at the graph below. What is the equation of this line?

What is the equation of this line?

xy-8-8-6-6-4-4-2-2224466880(0,−3)(2,1)
5

Look at the graph below. What is the equation of this line?

What is the equation of this line?

xy-8-8-6-6-4-4-2-2224466880(0,4)(4,2)
6

Look at the graph below. What is the equation of this line?

What is the equation of this line?

xy-8-8-6-6-4-4-2-2224466880(0,1)(1,4)
7

What is the slope of y = −4x − 9?

8

What is the y-intercept of y = x + 3?

9

Write the equation with slope 0 and y-intercept −5

10

A line has slope 2 and passes through (0, −1). Write its equation.

11

What is the y-intercept of y = 6x?

12

Write the equation with slope 1/2 and y-intercept 4

Finished all 12? Give yourself a pat on the back — then check your work!

Keep going — you're on a roll!

Every topic you master is another step on your journey.

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