IXL - Write a linear inequality from a graph (Algebra 1 practice)

This is the graph of a linear inequality. Write the inequality in slope-intercept form.

Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

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Learn with an example

question

This is the graph of a linear inequality. Write the inequality in slope-intercept form.

Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

key idea

The slope-intercept form of a linear equation is

where m is the slope and b is the

y-intercept.

To write a linear inequality in slope-intercept form, replace the equal sign with an inequality symbol. You can use this table to help you remember which inequality symbol to use.

	solid boundary line	dashed boundary line
shade above the line	y ≥ m x + b	y > m x + b
shade below the line	y ≤ m x + b	y < m x + b

solution

To write the inequality in slope-intercept form, start by identifying the

y-intercept,

and the slope,

of the boundary line.

The

y-intercept

is 6 because the boundary line crosses the

y-axis

(

)

You can use any two points on the boundary line to find the slope. For example, you can use

(

)

and

(

)

Divide the change in

y-coordinates

by the change in

x-coordinates

to find the slope.

Calculate the slope.

change in

–

The slope of the line is

–

and the

y-intercept

is 6. Plug these values into the slope-intercept formula.

–

Next, determine which inequality symbol to use by looking at the boundary line and the shaded area. The boundary line is

solid,

and the graph is shaded above the line. So, you should use the ≥ symbol.

This is the inequality written in slope-intercept form:

≥

–

Looking for more? Try these:

Lesson: Linear inequalities

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Teacher tools

Work it out

Not feeling ready yet? These can help:

L.5Slope-intercept form: write an equation from a graph

P.3Graph a two-variable linear inequality

Lesson: Linear inequalities

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