Question

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

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{4}{3}x - 1\), \(b=- 1\). So the line crosses the y - axis at the point \((0,-1)\). Plot the point \((0, - 1)\) on the coordinate plane.

Step2: Use the slope to find another point

The slope \(m=\frac{4}{3}\), which means for every 3 units we move to the right (increase in \(x\) by 3), we move up 4 units (increase in \(y\) by 4). Starting from \((0,-1)\), if we move 3 units to the right ( \(x = 0+3 = 3\)) and 4 units up ( \(y=-1 + 4=3\)), we get the point \((3,3)\). Plot the point \((3,3)\).

Step3: Draw the line

Use a straight - edge to draw a line passing through the points \((0,-1)\) and \((3,3)\). Extend the line in both directions to complete the graph of the line \(y=\frac{4}{3}x-1\).

Answer:

The line is graphed by plotting the y - intercept \((0,-1)\) and the point \((3,3)\) (found using the slope) and then drawing a straight line through these points (and extending it).