Point Slope Mastery Worksheet
Algebra 1 Practice
Point-Slope Form Mastery
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Formula \( y - y_1 = m(x - x_1) \)
\( m \) = Slope (\(\frac{\Delta y}{\Delta x}\))
\((x_1, y_1)\) = Given Point
Sign rule: \( x - (-3) \Rightarrow x + 3 \)
1
Deconstruct the Equation
Identify the slope and given point from each equation.
A. \( y - 5 = 2(x - 3) \)
Slope (\(m\)):
Point \((x_1, y_1)\):
B. \( y + 4 = -\frac{3}{4}(x - 6) \)
Slope (\(m\)):
Point \((x_1, y_1)\):
C. \( y - 1 = \frac{1}{2}(x + 7) \)
Slope (\(m\)):
Point \((x_1, y_1)\):
D. \( y + 8 = -(x + 2) \)
Slope (\(m\)):
Point \((x_1, y_1)\):
2
Write the Equation (Point & Slope)
Write each line's equation in point-slope form: \( y - y_1 = m(x - x_1) \).
A. Point: \((4, 1)\) | Slope: \( m = 3 \)
Point-Slope Form:
B. Point: \((-5, 6)\) | Slope: \( m = -\frac{2}{3} \)
Point-Slope Form:
C. Point: \((-2, -8)\) | Slope: \( m = \frac{5}{2} \)
Point-Slope Form:
D. Point: \((9, 0)\) | Slope: \( m = -4 \)
Point-Slope Form:
3
Write the Equation Given Two Points
Step 1: Find slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Step 2: Use either point to write the equation.
A. Passes through \((2, 3)\) and \((6, 11)\)
Show your slope calculation and equation setup below:
Calculated Slope \(m\):
Final Point-Slope Equation:
B. Passes through \((-3, 5)\) and \((1, -3)\)
Show your slope calculation and equation setup below:
Calculated Slope \(m\):
Final Point-Slope Equation:
Point-Slope Form Practice Page 1 of 2
Point-Slope Form: Graphing & Applications
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4
Graphing from Point-Slope Form
1. Plot the point \((x_1, y_1)\). 2. Count rise/run to plot a second point. 3. Draw line with arrows.
A. \( y - 1 = \frac{3}{2}(x - 2) \)
Point \((x_1, y_1)\):
Slope \(m\):
Rise / Run:
Check: Line slants upward left to right.
x y
B. \( y + 3 = -\frac{2}{3}(x + 1) \)
Point \((x_1, y_1)\):
Slope \(m\):
Rise / Run:
Check: Line slants downward left to right.
x y
5
Converting to Slope-Intercept Form
Distribute the slope and isolate \( y \) to express in \( y = mx + b \) form.
A. \( y - 4 = 3(x + 2) \)
\( y = mx + b \):
B. \( y + 5 = -2(x - 3) \)
\( y = mx + b \):
C. \( y - 7 = \frac{1}{2}(x - 8) \)
\( y = mx + b \):
6
Application & Error Analysis
A. Altitude Modeling
A research drone is descending at a constant rate of 15 feet per second. After 8 seconds of descent, its altitude is 420 feet.
1. Identify the given point \((t, a)\):
2. Identify the rate of change \(m\):
Point-Slope Eq:
B. Spot & Fix the Error
Problem: Write point-slope equation through \((-4, 7)\) with \(m = -2\).
Marcus's Work: \( y - 7 = -2(x - 4) \)
Explain Marcus's mistake and write the corrected equation:
Corrected Eq:
Point-Slope Form Practice Page 2 of 2
