Slopes and Intercepts

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

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

Example:

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.
Add $4x$ to both sides:
$2y = 4x + 8$

Step 2: Divide each term by 2 to solve for $y$:
$y = 2x + 4$

Step 3: Identify the slope and y-intercept.
From the equation $y = 2x + 4$:

• The slope $m = 2$
• The y-intercept $b = 4$
  This means the line rises 2 units for every 1 unit it moves to the right and crosses the y-axis at (0, 4).

Key Questions:

• What is the slope of the line represented by the equation $y = -3x + 5$?
• How would you find the y-intercept of the line $4x + 2y = 8$?
• If the slope of a line is 0, what can you say about the line?
• How do you graph the equation y = rac{1}{2}x - 3?
• What happens to the slope if you change the equation to y = -rac{1}{2}x - 3?

Keywords:

• Slope
• Y-intercept
• Linear function
• Slope-intercept form
• Graphing