Linear equations and inequalities (two variables)

Practice 5 items →

Three forms, one line. Students convert among slope-intercept, point-slope, and standard form, use parallel and perpendicular slope relations, and graph a linear inequality with the correct boundary style and half-plane.

Specification · for a parent or teacher
Part no.
linear-forms-half-planes
Course
High School Math 1 · Unit 5
Realm
Change
Difficulty
3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

convert among forms; graph linear inequalities (solid vs dashed, test point).

Ready when

line through (2,−1)(2,-1) perpendicular to y=2x+4y=2x+4, written in point-slope and slope-intercept.

Formulas

Point-slope
y−y1=m(x−x1)y - y_1 = m(x - x_1)
Standard form
Ax+By=CAx + By = C
Perpendicular slopes
m1m2=−1m_1 m_2 = -1

Watch for

perpendicular of m=2m=2 as m=−2m=-2; shading the wrong half-plane after a correct dashed line.

Before · requires

After · used by

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linear-forms-half-planes

Items: linear-forms-half-planes-01 · linear-forms-half-planes-02 · linear-forms-half-planes-03 · linear-forms-half-planes-04 · linear-forms-half-planes-05