Slope Workshop Slides Algebra Series
Slope
Workshop
Parallel & Perpendicular Lines
Today's Blueprint
01
Identify Slopes
Compare lines to see if they are parallel, perpendicular, or neither.
02
Build Equations
Use slope-intercept form to create equations for specific paths.
Slope-Intercept Form
y = mx + b
Slope Y-Intercept
Parallel Lines
The Geometry Rule
Parallel lines have the exact same slope.
Algebraic Example:
Line A: y = 3x + 5
Line B: y = 3x - 2
Slopes are both 3. They stay apart forever!
Perpendicular Lines
The Geometry Rule
Slopes are opposite reciprocals.
The Two-Step Flip:
Original 2
New -1/2
Flip the fraction (reciprocal) and switch the sign (opposite).
On Your Mark
Mission 01 Parallel
Write an equation for a line parallel to y = -4x + 1 that passes through (2, -5).
Teacher Guide:
The slope stays -4. Solve for b using -5 = -4(2) + b.
Mission 02 Perpendicular
Write an equation for a line perpendicular to y = 1/2x + 8 that passes through (5, -3).
Teacher Guide:
Slope of 1/2 flips to -2. Solve for b using -3 = -2(5) + b.
Slope Workshop Worksheet Slope Workshop
Parallel & Perpendicular Geometry
Student:
Date:
Parallel
Slopes are identical: \(m_1 = m_2\)
Perpendicular
Opposite reciprocals: \(m_1 \cdot m_2 = -1\)
01 Slope Detective
1. Slope parallel to \(y = 5x - 2\):
2. Slope perpendicular to \(y = \frac{1}{3}x + 7\):
3. Slope parallel to \(y = -\frac{2}{7}x + 10\):
4. Slope perpendicular to \(y = -4x - 5\):
02 Equation Builder
5. Parallel to \(y = 2x + 3\), passing through \((4, 1)\).
Show Work Here
Final Answer
6. Perpendicular to \(y = -3x - 1\), passing through \((-6, 2)\).
Show Work Here
Final Answer
7. Parallel to \(y = \frac{1}{2}x - 4\), passing through \((8, 10)\).
Show Work Here
Final Answer
8. Perpendicular to \(y = \frac{4}{5}x + 2\), passing through \((4, -3)\).
Show Work Here
Final Answer
03 Final Blueprint
9. Why do parallel lines have to have the exact same slope? Explain using geometry.
10. Find the equation of a line perpendicular to \(x = 5\) that passes through \((2, 3)\).
End of Workshop
Slope Workshop Answer Key Answer Key
Slope Workshop • Teacher Solutions
Verified
01: Slope Detective
1. Parallel to \(y = 5x - 2\): \(m = 5\)
2. Perp to \(y = \frac{1}{3}x + 7\): \(m = -3\)
3. Parallel to \(y = -\frac{2}{7}x + 10\): \(m = -\frac{2}{7}\)
4. Perp to \(y = -4x - 5\): \(m = \frac{1}{4}\)
02: Equation Builder
Problem 05 • Parallel to \(y = 2x + 3\) thru \((4, 1)\)
\(m = 2\)
\(1 = 2(4) + b \rightarrow 1 = 8 + b\)
\(b = -7\)
Final Equation \(y = 2x - 7\)
Problem 06 • Perp to \(y = -3x - 1\) thru \((-6, 2)\)
\(m = \frac{1}{3}\)
\(2 = \frac{1}{3}(-6) + b \rightarrow 2 = -2 + b\)
\(b = 4\)
Final Equation \(y = \frac{1}{3}x + 4\)
Problem 07 • Parallel to \(y = \frac{1}{2}x - 4\) thru \((8, 10)\)
\(m = \frac{1}{2}\)
\(10 = \frac{1}{2}(8) + b \rightarrow 10 = 4 + b\)
\(b = 6\)
Final Equation \(y = \frac{1}{2}x + 6\)
Problem 08 • Perp to \(y = \frac{4}{5}x + 2\) thru \((4, -3)\)
\(m = -\frac{5}{4}\)
\(-3 = -\frac{5}{4}(4) + b \rightarrow -3 = -5 + b\)
\(b = 2\)
Final Equation \(y = -\frac{5}{4}x + 2\)
03: Final Blueprint
9. If slopes were slightly different, the lines would eventually intersect. Parallel lines must have identical slopes to remain equidistant forever.
10. \(x = 5\) is vertical. Perpendicular must be horizontal (\(y = b\)). Passes through \((2, 3)\), so \(y = 3\).
