What do m and b stand for in y = mx + b?

m is the slope (rise over run) and b is the y-intercept, the y-value where the line crosses the y-axis.

Is y = mx + c the same as y = mx + b?

Yes. The UK usually writes c for the intercept and the US writes b. The meaning is identical.

Equation of a Straight Line: y = mx + b and Point-Slope Form

How to read slope and intercept from $y = mx + b$ , how to graph a line from its equation, and how to write the equation of a line from a point and a slope or from two points, including parallel and perpendicular lines.

3 min read Supports 4 lessons

A straight line is fixed by two facts: how steep it is, and where it is. The equation $y = mx + b$ stores exactly those two facts.

Slope-intercept form

y = mx + b

$m$ is the slope. $b$ is the $y$ -intercept: the line passes through $(0, b)$ . In the UK this is often written $y = mx + c$ .

Move the sliders and watch how each number controls the line.

Changing $m$ swings the line around its intercept. Changing $b$ slides the whole line up or down without changing its steepness.

Graphing from the equation

Key idea

Plot $(0, b)$ . Then step run 1, rise $m$ to find more points, and join them up.

Worked example

Graph $y = -2x + 3$ .

1
Start at the intercept, $(0, 3)$ .

Rearranging into this form

Equations are not always given as $y = \dots$ . Solve for $y$ and the slope and intercept appear.

$6x + 2y = 8$
Find the slope and $y$ -intercept.

1/4

Writing the equation of a line

If you know the slope $m$ and any one point $(x_1, y_1)$ on the line, point-slope form gives the equation straight away.

Point-slope form

y - y_1 = m(x - x_1)

Worked example

Find the line through $(2, 5)$ and $(4, 11)$ .

1
Slope.
$m = \frac{11 - 5}{4 - 2} = 3$

Tip

Check by substituting the other point: $3(4) - 1 = 11$ ✓.

Parallel and perpendicular lines

Parallel & perpendicular

\text{parallel: } m_1 = m_2 \qquad \text{perpendicular: } m_1 \cdot m_2 = -1

Same slope: parallel. Slopes $2$ and $-\frac{1}{2}$ : at right angles.

Watch out

Vertical lines cannot be written as $y = mx + b$ , because their slope is undefined. Their equations look like $x = 3$ .

Common questions

What do m and b stand for in y = mx + b?: $m$ is the slope (rise over run) and $b$ is the $y$ -intercept, the $y$ -value where the line crosses the $y$ -axis.
Is y = mx + c the same as y = mx + b?: Yes. The UK usually writes $c$ for the intercept and the US writes $b$ . The meaning is identical.

Practise equation of a line

The Slope-Intercept Form lesson has worked examples and unlimited practice that adapts to you.

Open the lesson

Graphs & Functions

Equation of a Straight Line: y = mx + b and Point-Slope Form

3 min read Supports 4 lessons

A straight line is fixed by two facts: how steep it is, and where it is. The equation $y = mx + b$ stores exactly those two facts.

Slope-intercept form

y = mx + b

$m$ is the slope. $b$ is the $y$ -intercept: the line passes through $(0, b)$ . In the UK this is often written $y = mx + c$ .

Move the sliders and watch how each number controls the line.

Changing $m$ swings the line around its intercept. Changing $b$ slides the whole line up or down without changing its steepness.

Graphing from the equation

Key idea

Plot $(0, b)$ . Then step run 1, rise $m$ to find more points, and join them up.

Worked example

Graph $y = -2x + 3$ .

1
Start at the intercept, $(0, 3)$ .

Rearranging into this form

Equations are not always given as $y = \dots$ . Solve for $y$ and the slope and intercept appear.

$6x + 2y = 8$
Find the slope and $y$ -intercept.

1/4

Writing the equation of a line

If you know the slope $m$ and any one point $(x_1, y_1)$ on the line, point-slope form gives the equation straight away.

Point-slope form

y - y_1 = m(x - x_1)

Worked example

Find the line through $(2, 5)$ and $(4, 11)$ .

1
Slope.
$m = \frac{11 - 5}{4 - 2} = 3$

Tip

Check by substituting the other point: $3(4) - 1 = 11$ ✓.

Parallel and perpendicular lines

Parallel & perpendicular

\text{parallel: } m_1 = m_2 \qquad \text{perpendicular: } m_1 \cdot m_2 = -1

Same slope: parallel. Slopes $2$ and $-\frac{1}{2}$ : at right angles.

Watch out

Vertical lines cannot be written as $y = mx + b$ , because their slope is undefined. Their equations look like $x = 3$ .

Common questions

What do m and b stand for in y = mx + b?: $m$ is the slope (rise over run) and $b$ is the $y$ -intercept, the $y$ -value where the line crosses the $y$ -axis.
Is y = mx + c the same as y = mx + b?: Yes. The UK usually writes $c$ for the intercept and the US writes $b$ . The meaning is identical.

Practise equation of a line

The Slope-Intercept Form lesson has worked examples and unlimited practice that adapts to you.

Open the lesson