Algebra 1 Graphing Linear Equations Test Solutions and Scoring (PDF)
This graphing linear test answers for Algebra 1 covers graphing linear equations (Common Core A-REI.D.10, F-IF.C.7a, A-CED.A.2), with a free PDF to print.
Algebra 1 · Common Core State Standards: A-REI.D.10, F-IF.C.7a, A-CED.A.2
Graphing linear test answers: worked solutions
Question 1 – Slope and intercept [2 pts]
a) Slope \(-4\), y-intercept \((0, 7)\).
b) Slope \(\frac{3}{5}\), y-intercept \((0, -2)\).
Scoring: 1 point for each part (both values correct).
Question 2 – Graph a line [2 pts]
Plot the y-intercept \((0, -1)\). The slope is \(\frac{3}{4}\): up 3, right 4 to \((4, 2)\). Draw the line.
Scoring: 1 point for the correct y-intercept; 1 point for the correct slope and line.
Question 3 – Find intercepts [2 pts]
Let \(y = 0\): \(5x = 20\), so \(x = 4\).
Let \(x = 0\): \(-2y = 20\), so \(y = -10\).
(4, 0) and (0, -10)
Scoring: 1 point for each intercept.
Question 4 – Rewrite an equation [2 pts]
Subtract \(4x\): \(2y = -4x + 10\). Divide by 2.
\(y = -2x + 5\)
Scoring: 1 point for isolating the y-term; 1 point for dividing every term.
Question 5 – Point-slope form [2 pts]
Point-slope: \(y – 5 = -3(x – 2)\).
Distribute: \(y – 5 = -3x + 6\), so \(y = -3x + 11\).
\(y – 5 = -3(x – 2)\); \(y = -3x + 11\)
Scoring: 1 point for each form.
Question 6 – Equation from a graph [2 pts]
The y-intercept is 6. From \((0, 6)\) to \((2, 3)\), the level changes by -3 in 2 hours.
\(y = -\frac{3}{2}x + 6\)
Scoring: 1 point for the slope; 1 point for the equation.
Question 7 – Data plan [3 pts]
a) Slope \(\frac{0 – 12}{8 – 0} = -1.5\), so \(y = -1.5x + 12\).
b) The x-intercept \((8, 0)\) means all the data is used after 8 days.
c) \(y = -1.5(4) + 12 = 6\) GB.
\(y = -1.5x + 12\); 8 days; 6 GB
Scoring: 1 point per part.
Question 8 – Points on a line [3 pts]
a) \(2(6) – 3(0) = 12\) true. \(2(0) – 3(4) = -12\) false. \(2(-3) – 3(-6) = -6 + 18 = 12\) true. \(2(5) – 3(1) = 7\) false.
b) \(18 – 3y = 12\), so \(-3y = -6\) and \(y = 2\).
\((6, 0)\) and \((-3, -6)\); \(y = 2\)
Scoring: part a, 1 point for testing all points and 1 point for the correct two; part b, 1 point.
Question 9 – Horizontal and vertical [2 pts]
Every point on the horizontal line has y-coordinate -3. Every point on the vertical line has x-coordinate 4.
\(y = -3\) and \(x = 4\)
Scoring: 1 point for each equation.
Total score
20 points
Key facts behind this graphing linear test answers
- Every point on the line is a solution of the equation, and every solution is on the line.
- In y = mx + b, m is the slope and b is the y-intercept.
- Find intercepts by setting x = 0 for the y-intercept and y = 0 for the x-intercept.
- Point-slope form y – y₁ = m(x – x₁) uses a known point and the slope.
- y = k is horizontal with slope 0; x = h is vertical with undefined slope.
How to use this graphing linear test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
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