Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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Transcribed Image Text:**Sketch a Graph of \( f(x) = \frac{3}{2}x + 2 \)**
The image presents the equation of a linear function \( f(x) = \frac{3}{2}x + 2 \) and includes a coordinate plane with both x and y axes ranging from -5 to 5.
### Key Components:
1. **Equation**:
The given equation is \( f(x) = \frac{3}{2}x + 2 \), which is in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.
2. **Coordinate Grid**:
- The x-axis and y-axis both span from -5 to 5.
- The grid is drawn in a standard Cartesian plane format with horizontal and vertical lines marking intervals of 1 unit.
3. **Graphing Tools**:
Below the coordinate plane, there are options to draw various types of graphs and objects:
- Linear function (highlighted)
- Quadratic function
- Piecewise function
- Circle
- Point indicator
- There is also a "Clear All" button to reset the graph.
### Step-by-Step Graphing Explanation:
1. **Identify the y-intercept**:
- The y-intercept \( b \) is 2. This tells us that the point (0, 2) is on the graph. You can plot this point on the y-axis where y is 2.
2. **Determine the slope**:
- The slope \( m \) is \( \frac{3}{2} \). This means for every 2 units you move right along the x-axis, you move up 3 units along the y-axis.
3. **Plot Additional Points Using the Slope**:
- From the y-intercept (0, 2), move 2 units right to x = 2, then move up 3 units (y + 3), which leads to the point (2, 5).
- Alternatively, for every 2 units you move left along the x-axis, you move down 3 units along the y-axis, leading to other points such as (-2, -1).
4. **Draw the Line**:
- Once you have plotted several points, draw a straight line through these points to represent the
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