Slope Review Practice Worksheet Pre-Algebra • Slope Review
Finding Slope from a Graph
Name:
Date:
Period:
Part 1: Find the slope of each line using the marked points.
Slope \(m = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1}\)
1 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
2 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
3 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
4 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
5 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
6 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
7 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
8 Count rise & run
x y
Pt 1: (__, __)
Pt 2: (__, __)
Rise: Run:
\(m =\)
Tip: Rise = change in \(y\) (up is +, down is −). Run = change in \(x\) (right is +).
Page 1 of 2
Pre-Algebra • Slope Practice
Slope from Points & Equations
Name:
Date:
Per:
Part 2: Find the slope of the line through each pair of points. \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\((8, 10)\) and \((-7, 14)\)
\(m =\)
\((-3, 1)\) and \((-17, 2)\)
\(m =\)
\((-20, -4)\) and \((-12, -10)\)
\(m =\)
\((-12, -5)\) and \((0, -8)\)
\(m =\)
\((-19, -6)\) and \((15, 16)\)
\(m =\)
\((-6, 9)\) and \((7, -9)\)
\(m =\)
\((-18, -20)\) and \((-18, -15)\)
\(m =\)
\((12, -18)\) and \((11, 12)\)
\(m =\)
Part 3: Find the slope of each line. Slope-Intercept Form: \(y = mx + b\)
\(y = -5x - 1\)
\(m =\)
\(y = \frac{1}{3}x - 4\)
\(m =\)
\(y = -\frac{1}{5}x - 4\)
\(m =\)
\(x = 1\)
\(m =\)
\(y = \frac{1}{4}x + 1\)
\(m =\)
\(y = -\frac{2}{3}x - 1\)
\(m =\)
\(y = -x + 2\)
\(m =\)
\(y = -x - 1\)
\(m =\)
\(2x + 3y = 9\) Solve for \(y\)
Final Slope:
\(m =\)
\(5x + 2y = 6\) Solve for \(y\)
Final Slope:
\(m =\)
Completed all 26 review problems! Be sure all fractions are fully simplified. Page 2 of 2
Slope Review Answer Key Teacher Resource • Answer Key
Finding Slope from a Graph • Solutions
Full Answer Key
Part 1: Marked point coordinates, rise/run counts, and simplified slopes.
\(m = \frac{\text{Rise}}{\text{Run}} = \frac{\Delta y}{\Delta x}\)
1 Falls left to right (\(-\))
x y
Pt 1: (0, −1)
Pt 2: (4, −2)
Rise: −1 Run: +4
\(m =\) \(-\frac{1}{4}\)
2 Rises left to right (+)
x y
Pt 1: (0, −1)
Pt 2: (1, 2)
Rise: +3 Run: +1
\(m =\) \(3\)
3 Falls left to right (\(-\))
x y
Pt 1: (−3, 1)
Pt 2: (0, −3)
Rise: −4 Run: +3
\(m =\) \(-\frac{4}{3}\)
4 Rises left to right (+)
x y
Pt 1: (0, −2)
Pt 2: (3, 2)
Rise: +4 Run: +3
\(m =\) \(\frac{4}{3}\)
5 Rises left to right (+)
x y
Pt 1: (−2, −3)
Pt 2: (0, 1)
Rise: +4 Run: +2
\(m =\) \(\frac{4}{2} = 2\)
6 Rises left to right (+)
x y
Pt 1: (1, −4)
Pt 2: (3, 2)
Rise: +6 Run: +2
\(m =\) \(\frac{6}{2} = 3\)
7 Falls left to right (\(-\))
x y
Pt 1: (0, 3)
Pt 2: (1, −1)
Rise: −4 Run: +1
\(m =\) \(-4\)
8 Rises left to right (+)
x y
Pt 1: (−2, −4)
Pt 2: (0, 2)
Rise: +6 Run: +2
\(m =\) \(\frac{6}{2} = 3\)
Part 1 Solutions Complete • Check student work for proper integer signs on rise and run. Page 1 of 2
Pre-Algebra • Slope Practice
Points & Equations Solutions • Answer Key
Page 2 Solutions
Part 2: Slope Through Each Pair of Points (Formula Substitution) \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\((8, 10)\) and \((-7, 14)\)
Two Point Slope Worksheet Pre-Algebra • Slope Formula Guide
Finding Slope Between Two Points
Name:
Date:
Period:
Step 1: Label \((x_1, y_1)\) & \((x_2, y_2)\)
Step 2: Substitute \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Step 3: Subtract Watch negative signs!
Step 4: Simplify Reduce fraction fully
Worked Examples • Walkthrough
Example 1: Positive Coordinates \((2, 3)\) and \((6, 11)\)
1 Label: \(x_1 = 2,\; y_1 = 3 \quad x_2 = 6,\; y_2 = 11\)
2 Formula: \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - 3}{6 - 2}\)
3 Subtract: \(m = \frac{8}{4}\)
Final Answer: \(m = 2\)
Example 2: Negative Signs \((-3, 5)\) and \((1, -3)\)
1 Label: \(x_1 = -3,\; y_1 = 5 \quad x_2 = 1,\; y_2 = -3\)
2 Formula: \(m = \frac{-3 - 5}{1 - (-3)}\)
3 Watch double negative: \(1 - (-3) = 1 + 3 = 4\)
Simplify \(\frac{-8}{4}\): \(m = -2\)
Key Special Cases:
Horizontal Line: \(\frac{0}{\text{any}} = \mathbf{0}\) (Zero Slope)
Vertical Line: \(\frac{\text{any}}{0} = \mathbf{\text{Undefined}}\)
Guided Practice: Label coordinates and show each step Apply the 4-step formula
\((1, 2)\) and \((5, 10)\) Step 1: Fill in
\(x_1 = \underline{\hspace{1.5cm}},\; y_1 = \underline{\hspace{1.5cm}} \quad x_2 = \underline{\hspace{1.5cm}},\; y_2 = \underline{\hspace{1.5cm}}\)
Final Slope:
\(m =\)
\((-2, 4)\) and \((4, -8)\) Step 1: Fill in
\(x_1 = \underline{\hspace{1.5cm}},\; y_1 = \underline{\hspace{1.5cm}} \quad x_2 = \underline{\hspace{1.5cm}},\; y_2 = \underline{\hspace{1.5cm}}\)
Final Slope:
\(m =\)
\((-5, -3)\) and \((0, 7)\) Step 1: Fill in
\(x_1 = \underline{\hspace{1.5cm}},\; y_1 = \underline{\hspace{1.5cm}} \quad x_2 = \underline{\hspace{1.5cm}},\; y_2 = \underline{\hspace{1.5cm}}\)
Final Slope:
\(m =\)
\((3, -6)\) and \((-1, -6)\) Step 1: Fill in
\(x_1 = \underline{\hspace{1.5cm}},\; y_1 = \underline{\hspace{1.5cm}} \quad x_2 = \underline{\hspace{1.5cm}},\; y_2 = \underline{\hspace{1.5cm}}\)
Final Slope:
\(m =\)
Turn over for Independent Practice • Remember: \(y\) is in the numerator, \(x\) is in the denominator. Page 1 of 2
Two Point Slope Answer Key Teacher Resource • Answer Key
Finding Slope Between Two Points • Solutions
Full Solutions Key
Step 1: Label \((x_1, y_1)\) & \((x_2, y_2)\)
Step 2: Substitute \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Step 3: Subtract Watch double negatives!
Step 4: Simplify Reduce to lowest terms
Reference Walkthrough
Example 1: Positive Values \((2, 3)\) and \((6, 11)\)
1 Label: \(x_1 = 2,\; y_1 = 3 \quad x_2 = 6,\; y_2 = 11\)
2 Formula: \(m = \frac{11 - 3}{6 - 2} = \frac{8}{4}\)
3 Simplify: \(8 \div 4 = 2\)
Slope Result: \(m = 2\)
Example 2: Negative Numbers \((-3, 5)\) and \((1, -3)\)
1 Label: \(x_1 = -3,\; y_1 = 5 \quad x_2 = 1,\; y_2 = -3\)
2 Formula: \(m = \frac{-3 - 5}{1 - (-3)} = \frac{-8}{1 + 3}\)
3 Simplify: \(-8 \div 4 = -2\)
Slope Result: \(m = -2\)
Key Rules:
Horizontal: \(\frac{0}{k} = \mathbf{0}\) (Zero Slope)
Vertical: \(\frac{k}{0} = \mathbf{\text{Undefined}}\)
Guided Practice • Complete Worked Solutions Problems 1–4
\((1, 2)\) and \((5, 10)\) Positive
\(x_1 = \mathbf{1},\; y_1 = \mathbf{2} \quad x_2 = \mathbf{5},\; y_2 = \mathbf{10}\)
\(m = \frac{10 - 2}{5 - 1} = \frac{8}{4}\)
\(= 2\)
Final Slope:
\(m =\) \(2\)
\((-2, 4)\) and \((4, -8)\) Negative
\(x_1 = \mathbf{-2},\; y_1 = \mathbf{4} \quad x_2 = \mathbf{4},\; y_2 = \mathbf{-8}\)
\(m = \frac{-8 - 4}{4 - (-2)} = \frac{-12}{4 + 2} = \frac{-12}{6}\)
\(= -2\)
Final Slope:
\(m =\) \(-2\)
\((-5, -3)\) and \((0, 7)\) Positive
\(x_1 = \mathbf{-5},\; y_1 = \mathbf{-3} \quad x_2 = \mathbf{0},\; y_2 = \mathbf{7}\)
\(m = \frac{7 - (-3)}{0 - (-5)} = \frac{7 + 3}{0 + 5} = \frac{10}{5}\)
\(= 2\)
Final Slope:
\(m =\) \(2\)
\((3, -6)\) and \((-1, -6)\) Zero Slope
\(x_1 = \mathbf{3},\; y_1 = \mathbf{-6} \quad x_2 = \mathbf{-1},\; y_2 = \mathbf{-6}\)
\(m = \frac{-6 - (-6)}{-1 - 3} = \frac{-6 + 6}{-4} = \frac{0}{-4}\)
\(= 0\) (Horizontal Line)
Final Slope:
\(m =\) \(0\)
Figure Translations Practice Worksheet Geometry • Transformations
Translations on the Coordinate Plane
Name:
Date:
Period:
Rule: \((x, y) \to (x + h, y + k)\)
Horizontal: \(+h\) (Right) • \(-h\) (Left) Vertical: \(+k\) (Up) • \(-k\) (Down)
1 translation: \((x, y) \to (x - 2, y - 1)\)
Shift: 2 Left, 1 Down
Given Pre-image K L M K(-1,2) L(3,4) M(1,-1)
Choice A
K' L' M' Shifted down 3
Choice B
K' L' M' Shifted down 2
Choice C
K' L' M' Shifted 2L, 1D
Image: \(K'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; L'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; M'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}})\)
Answer: A B C
2 translation: \((x, y) \to (x + 3, y - 5)\)
Shift: 3 Right, 5 Down
Given Pre-image D E F D(-5,1) E(-1,5) F(-1,1)
Choice A
D' E' F' Shifted 6R, 5D
Choice B
D' E' F' Shifted 3R, 5D
Choice C
D' E' F' Shifted 3R, 1D
Image: \(D'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; E'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; F'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}})\)
Answer: A B C
3 translation: \((x, y) \to (x + 6, y - 2)\)
Shift: 6 Right, 2 Down
Given Pre-image V W X V(-5,3) W(-1,4) X(-3,1)
Choice A
V' W' X' Shifted 6R, 2D
Choice B
V' W' X' Shifted 4R, 2D
Choice C
V' W' X' Shifted 6R, 4D
Image: \(V'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; W'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; X'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}})\)
Answer: A B C
Compare each option's vertex coordinates to find the exact matching transformation. Page 1 of 2
Geometry • Transformations
Translations Practice • Page 2
Name:
Per:
4 translation: \((x, y) \to (x + 2, y + 2)\)
Shift: 2 Right, 2 Up
Given Pre-image S R Q S(-1,-3) R(-1,3) Q(3,0)
Choice A
S' R' Q' Shifted 1R, 2U
Choice B
S' R' Q' Shifted 2R, 2U
Choice C
S' R' Q' Shifted 2R, 1U
Image: \(S'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; R'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}}),\; Q'(\underline{\hspace{0.8cm}}, \underline{\hspace{0.8cm}})\)
