Step-by-Step Examples: Finding Slope and Y-Intercept

📚 Quick Study Guide

• 📈 Slope: The slope ($m$) of a line represents its steepness and direction. It's calculated as the change in $y$ divided by the change in $x$ (rise over run). The formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ given two points $(x_1, y_1)$ and $(x_2, y_2)$.
• 📍 Y-Intercept: The y-intercept ($b$) is the point where the line crosses the y-axis. It's the value of $y$ when $x = 0$.
• ✏️ Slope-Intercept Form: The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• ➕ Finding Slope from an Equation: If the equation is in the form $y = mx + b$, simply identify the coefficient of $x$ as the slope ($m$).
• ✂️ Finding Y-Intercept from an Equation: If the equation is in the form $y = mx + b$, the constant term ($b$) is the y-intercept.
• ✍️ Finding Slope and Y-Intercept from Two Points: First, calculate the slope using the slope formula. Then, substitute one of the points and the calculated slope into the equation $y = mx + b$ and solve for $b$.

Practice Quiz

1. What is the slope of the line passing through the points (2, 5) and (4, 9)?

   1. -2
   2. 2
   3. 1/2
   4. -1/2

2. What is the y-intercept of the line $y = 3x - 2$?

   1. 3
   2. -2
   3. 2
   4. -3

3. What is the slope of the line $y = -2x + 5$?

   1. 5
   2. 2
   3. -2
   4. -5

4. What is the y-intercept of the line passing through the points (0, 3) and (1, 5)?

   1. 5
   2. 2
   3. 3
   4. 0

5. The equation of a line is $y = \frac{1}{2}x + 4$. What is the slope?

   1. 4
   2. 2
   3. $\frac{1}{2}$
   4. -$\frac{1}{2}$

6. What is the y-intercept of the line $y = -x - 7$?

   1. -1
   2. 7
   3. -7
   4. 1

7. What is the slope of the line passing through the points (1, 2) and (1, 7)?

   1. 0
   2. 5
   3. Undefined
   4. 1