Question

graph the line.
$y=\frac{4}{3}x - 1$

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m=\frac{4}{3}\) (slope) and \(b = - 1\) (y - intercept).

Step2: Plot the y - intercept

The y - intercept is \((0,-1)\). So we mark the point \((0, - 1)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{4}{3}\) means "rise over run", or \(\frac{\text{change in }y}{\text{change in }x}\). From the point \((0,-1)\), we move up 4 units (since the numerator of the slope is 4) and then move to the right 3 units (since the denominator of the slope is 3). This gives us the point \((0 + 3,-1+4)=(3,3)\). We can also move down 4 units and left 3 units from \((0,-1)\) to get another point \((0 - 3,-1-4)=(-3,-5)\).

Step4: Draw the line

Using a straight - edge, we draw a line that passes through the points we plotted (e.g., \((0,-1)\) and \((3,3)\) or \((0,-1)\) and \((-3,-5)\)).

Answer:

To graph the line \(y=\frac{4}{3}x - 1\):

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