Linear Equations Conversion Worksheet
Algebra 1 • Linear Functions
Linear Equations Conversion Worksheet
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Slope: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Point-Slope: \(y - y_1 = m(x - x_1)\)
Slope-Intercept: \(y = mx + b\)
Standard: \(Ax + By = C\)
Directions: For each pair of points, calculate the slope \(m\), write in point-slope form, solve for slope-intercept form, and convert to standard form (\(A \ge 0\), integers).
Page 1 of 5
1. Given: \((2, 3)\) and \((4, 7)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
2. Given: \((1, 4)\) and \((3, 10)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
3. Given: \((-1, -1)\) and \((2, 8)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
4. Given: \((0, 4)\) and \((2, 8)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
5. Given: \((3, 2)\) and \((7, 6)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
6. Given: \((1, -2)\) and \((5, 14)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
Linear Equations Conversion Worksheet • Problems 7–12
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Page 2 of 5
7. Given: \((1, 7)\) and \((3, 3)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
8. Given: \((-2, 9)\) and \((1, 0)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
9. Given: \((2, -1)\) and \((6, -5)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
10. Given: \((0, 5)\) and \((4, -3)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
11. Given: \((-3, 11)\) and \((2, -9)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
12. Given: \((4, 1)\) and \((7, -14)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
Linear Equations Conversion Worksheet • Problems 13–18
Name:
Page 3 of 5
13. Given: \((2, 5)\) and \((6, 7)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
14. Given: \((-4, 1)\) and \((2, 4)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
15. Given: \((2, 5)\) and \((6, 3)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
16. Given: \((-3, -2)\) and \((3, 0)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
17. Given: \((3, 7)\) and \((6, 6)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
18. Given: \((-4, -3)\) and \((4, -1)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
Linear Equations Conversion Worksheet • Problems 19–24
Name:
Page 4 of 5
19. Given: \((3, 1)\) and \((6, 3)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
20. Given: \((-3, 7)\) and \((3, 3)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
21. Given: \((4, 1)\) and \((8, 4)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
22. Given: \((-4, 8)\) and \((4, 2)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
23. Given: \((2, 1)\) and \((4, 4)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
24. Given: \((-2, 7)\) and \((2, 1)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
Linear Equations Conversion Worksheet • Problems 25–30
Name:
Page 5 of 5
25. Given: \((-5, -2)\) and \((5, 6)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
26. Given: \((-5, 9)\) and \((5, 3)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
27. Given: \((-2, 4)\) and \((4, 4)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
28. Given: \((1, 2)\) and \((4, 7)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
29. Given: \((-2, 5)\) and \((3, -2)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
30. Given: \((2, -3)\) and \((5, 1)\) Work Area
Slope (\(m\)):
\(y\)-int (\(b\)):
Slope-Int (\(y = mx + b\)):
Standard Form (\(Ax + By = C\)):
