Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
The last six problems build linear models from stories (F-LE.A.1a, F-LE.A.2 and A-CED.A.2): memberships, hikes, candles, budgets and draining pools.
Standards: F-IF.C.7a, F-LE.A.1a, F-LE.A.2, A-CED.A.2 · Level: Grade 9 Algebra 1
Problem 1 Slope from two points ★★★
Find the slope of the line through (7, −5) and (13, 19).
Problem 2 Negative slope ★★★
Find the slope of the line through (−1, 4) and (5, −2).
Problem 3 Read slope and intercept ★★★
Name the slope and the y-intercept in y = −8x + 15.
Problem 4 Write from slope and intercept ★★★
Write the equation of the line with slope 6 and y-intercept −11.
Problem 5 Equation from a graph ★★★
The graph of a line is shown with two points plotted. Describe its slope and write its equation in the form y = mx + b.
Problem 6 Point-slope form ★★★
Write an equation of the line with slope 3 through (2, −1) in point-slope form, then in slope-intercept form.
Problem 7 Line through two points ★★★
A line passes through (−4, 9) and (6, −11). Write its equation in slope-intercept form.
Problem 8 Standard to slope-intercept ★★★
Rewrite 4x + 2y = 10 in slope-intercept form and give both intercepts.
Problem 9 Slope-intercept to standard ★★★
Write y = 23x − 4 in standard form with integer coefficients.
Problem 10 Graph from intercepts ★★★
Graph 3x − 4y = 12 by finding its intercepts.
Problem 11 Parallel line ★★★
Write the equation of the line through (3, 9) that is parallel to y = 2x − 1.
Problem 12 Perpendicular line ★★★
Write the equation of the line through (6, 1) that is perpendicular to y = 3x + 8.
Problem 13 Parallel, perpendicular or neither ★★★
Classify each pair of lines. (a) y = 3x − 2 and 6x − 2y = 5 (b) y = 34x + 1 and 4x + 3y = 7.
Problem 14 Is the table linear? ★★★
Decide whether the table is linear and, if so, write a rule.
| x | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| y | 5 | 11 | 17 | 23 |
Problem 15 Fitness membership ★★★
A studio charges $40 to join plus $22 each month. Write a function C(m) for the total cost after m months, find the cost after 7 months, and interpret the slope and the intercept.
Problem 16 Hiker’s elevation ★★★
A hiker’s elevation is 1,900 feet after 2 hours and 2,950 feet after 5 hours, climbing at a steady rate. Write an equation for the elevation E after t hours and find when the hiker reaches 4,000 feet.
Problem 17 Burning candle ★★★
A candle is 12 inches tall and burns down 0.75 inch each hour. Write H(t) for its height, state the domain and range, and find when it burns out. Use the graph.
Problem 18 School store budget ★★★
A school store spends exactly $20 on pencils at $0.50 each and notebooks at $2 each. Write an equation in standard form with integer coefficients, find the intercepts, and find how many notebooks go with 12 pencils. Use the graph.
Problem 19 Draining a pool ★★★
A pool holds 450 gallons after 3 minutes of draining and 200 gallons after 8 minutes. Write an equation for the gallons G left after t minutes, find how much water the pool began with and when it is empty.
Problem 20 Right angle test ★★★
Triangle ABC has vertices A(0, 0), B(6, 2) and C(5, 5). Use slopes to decide whether the angle at B is a right angle.
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