graphing equation of a straight line y= mx + c

An SAT Math micro-topic under Graphs of linear systems and inequalities (Algebra). Free to read — no account needed.

A straight line is fixed by any two points, so to graph one you find two points and connect them. The intercepts — where the line meets the axes — are usually the easiest pair to find.

In the figure, the line

y = -2x + 4

is drawn through its intercepts. Set

x = 0

for the

y

-intercept

(0, 4)

, and set

y = 0

for the

x

-intercept

(2, 0)

You can also use slope-intercept form directly: in

y = mx + c

, the value

c

is the

y

-intercept, so plot

(0, c)

first, then use the slope

m

as rise over run to step to a second point. For

y = 2x + 3

, plot

(0, 3)

, then go up

2

and right

1

(1, 5)

If the line is given in a rearranged form like

2x - 3y + 3 = 0

, just find the two intercepts directly: at

y = 0

2x + 3 = 0

x = -\frac{3}{2}

; at

x = 0

-3y + 3 = 0

y = 1

Worked examples

Graph

y = 3x - 6

using its intercepts.

y

-intercept (set

x = 0

(0, -6)

x

-intercept (set

y = 0

0 = 3x - 6

, so

x = 2

, giving

(2, 0)

. Draw the line through these two points.

Graph

-2x + 4y = 8

using its intercepts.

x

-intercept (set

y = 0

-2x = 8

, so

x = -4

, the point

(-4, 0)

y

-intercept (set

x = 0

4y = 8

, so

y = 2

, the point

(0, 2)

Graph

y = -\frac{1}{2}x + 4

using the slope.
Start at the

y

-intercept

(0, 4)

.
The slope is

-\frac{1}{2}

, so go down

1

and right

2

(2, 3)

. Draw the line through both points.

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graphing equation of a straight line y= mx + c

Worked examples

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