Question

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

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{3}{4}x - 2\), \(b=-2\). So the line crosses the y - axis at the point \((0,-2)\). We plot this point on the graph.

Step2: Use the slope to find another point

The slope \(m=\frac{3}{4}\), which means for a run of 4 (change in \(x\)), the rise is 3 (change in \(y\)). Starting from the y - intercept \((0,-2)\), if we move 4 units to the right (increase \(x\) by 4) to \(x = 4\), and then 3 units up (increase \(y\) by 3), we get \(y=-2 + 3=1\). So the point \((4,1)\) is on the line. We can also use a run of - 4 (move 4 units to the left) and a rise of - 3 (move 3 units down). Starting from \((0,-2)\), moving 4 units left to \(x=-4\) and 3 units down gives \(y=-2-3=-5\), so the point \((-4,-5)\) is also on the line.

Step3: Draw the line

Using a straight - edge, draw a line through the points we found (e.g., \((0,-2)\), \((4,1)\), \((-4,-5)\)) to represent the line \(y=\frac{3}{4}x - 2\).

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y = \frac{3}{4}x-2\) passing through the points like \((0, - 2)\), \((4,1)\), \((-4,-5)\) etc. But in the format, we can describe the process of graphing as above.)

Answer:

The graph of the line \(y=\frac{3}{4}x - 2\) is drawn by first plotting the y - intercept \((0,-2)\), then using the slope \(\frac{3}{4}\) to find additional points (e.g., \((4,1)\), \((-4,-5)\)) and drawing a straight line through these points.