Question

graph the equation $y = -\frac{3}{2}x + 4$.

Explanation:

Step1: Identify the slope and y - intercept

The equation \(y = -\frac{3}{2}x + 4\) is in the slope - intercept form \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Here, the slope \(m = -\frac{3}{2}\) and the y - intercept \(b = 4\). So, the line crosses the y - axis at the point \((0,4)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,4)\) (since when \(x = 0\), \(y=4\)) and mark it.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{2}=\frac{\text{change in }y}{\text{change in }x}\). This means that from the y - intercept \((0,4)\), we can move down 3 units (because the numerator is - 3, which represents a decrease in \(y\)) and then move 2 units to the right (because the denominator is 2, which represents an increase in \(x\)). So, starting from \((0,4)\), moving down 3 units gives \(y = 4-3 = 1\) and moving 2 units to the right gives \(x=0 + 2=2\). So, we get the point \((2,1)\). We can also move up 3 units and left 2 units (since a negative slope can also be thought of as \(\frac{3}{-2}\)). Starting from \((0,4)\), moving up 3 units gives \(y = 4 + 3=7\) and moving left 2 units gives \(x=0-2=-2\), so we get the point \((-2,7)\).

Step4: Draw the line

Connect the points (such as \((0,4)\) and \((2,1)\) or \((0,4)\) and \((-2,7)\)) with a straight line to graph the equation \(y=-\frac{3}{2}x + 4\).

Answer:

To graph \(y = -\frac{3}{2}x+4\):

1. Plot the y - intercept \((0,4)\).
2. Use the slope \(-\frac{3}{2}\) to find another point (e.g., from \((0,4)\), move down 3, right 2 to get \((2,1)\) or up 3, left 2 to get \((-2,7)\)).
3. Draw a straight line through the plotted points.