Question

graph $y = 0.75x - 0.5$. line undo redo × reset

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m = 0.75=\frac{3}{4}\) (slope) and \(b=- 0.5\) (y - intercept).

Step2: Plot the y - intercept

The y - intercept is \(b=-0.5\), so we plot the point \((0,-0.5)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=\frac{3}{4}\) means "rise over run", so from the point \((0, - 0.5)\), we move up 3 units and then right 4 units (or down 3 units and left 4 units). Moving up 3 units from \(y=-0.5\) gives \(y=-0.5 + 3=2.5\), and moving right 4 units from \(x = 0\) gives \(x = 4\). So we get the point \((4,2.5)\). We can also use a smaller "run" and "rise" by considering the slope as \(\frac{3}{4}=\frac{0.75}{1}\), so from \((0,-0.5)\), moving up 0.75 units and right 1 unit gives the point \((1,0.75 - 0.5)=(1,0.25)\).

Step4: Draw the line

Draw a straight line through the two (or more) points we found (e.g., \((0,-0.5)\) and \((4,2.5)\) or \((0,-0.5)\) and \((1,0.25)\)) to graph the line \(y = 0.75x-0.5\).

Answer:

To graph \(y = 0.75x-0.5\), plot the y - intercept \((0,-0.5)\) and then use the slope \(\frac{3}{4}\) to find another point (e.g., \((4,2.5)\) or \((1,0.25)\)) and draw a line through these points. The line passes through \((0,-0.5)\) and has a positive slope of \(0.75\).