In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = (3/4)x-2

Verified step by step guidance

1. Step 1: Identify the form of the linear equation. The given equation is f(x) = \frac{3}{4}x - 2, which is in the slope-intercept form y = mx + b.
2. Step 2: Determine the slope (m) of the line. In the equation y = mx + b, m represents the slope. Here, m = \frac{3}{4}.
3. Step 3: Determine the y-intercept (b) of the line. In the equation y = mx + b, b represents the y-intercept. Here, b = -2.
4. Step 4: To graph the linear function, start by plotting the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis, which is (0, -2).
5. Step 5: Use the slope to find another point on the line. The slope \frac{3}{4} means that for every 4 units you move to the right along the x-axis, you move 3 units up along the y-axis. From the y-intercept (0, -2), move 4 units to the right and 3 units up to find another point on the line.

Key Concepts

Slope

The slope of a line measures its steepness and direction, represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. In the equation f(x) = (3/4)x - 2, the slope is 3/4, indicating that for every 4 units moved horizontally to the right, the line rises 3 units vertically.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form. In the equation f(x) = (3/4)x - 2, the y-intercept is -2, meaning the line intersects the y-axis at the point (0, -2).

Graphing Linear Functions

Graphing a linear function involves plotting points that satisfy the equation and drawing a straight line through them. Starting with the y-intercept (0, -2), you can use the slope (3/4) to find another point by moving up 3 units and right 4 units, allowing for a clear representation of the linear relationship.