Slopes and Intercepts

In this lesson, we will explore linear equations, focusing on slopes and intercepts. A linear equation can be written in the slope-intercept form: $y = mx + b$, where:

• $m$ is the slope of the line.
• $b$ is the y-intercept, the point where the line crosses the y-axis.

Example Problem

Find the slope and y-intercept of the line represented by the equation: $2y - 4x = 8$.

Step 1: Rearrange the equation into slope-intercept form.

$2y = 4x + 8$

Step 2: Divide every term by 2 to isolate $y$.

$y = 2x + 4$

Step 3: Identify the slope and y-intercept.

• Slope ($m$) = 2
• Y-intercept ($b$) = 4

Thus, the slope of the line is 2, and the line crosses the y-axis at (0, 4).

Key Questions

• What is the slope of the line represented by the equation $y = -3x + 1$?
• Where does the line y = rac{1}{2}x - 5 intersect the y-axis?
• How can you determine if a line is increasing or decreasing based on its slope?
• If a line has a slope of 0, what type of line is it?

Keywords

• Slope
• Y-intercept
• Linear equation
• Slope-intercept form
• Increasing/decreasing