Question

graph $f(x) = \frac{3}{4}x + 2$. use the line tool and select two points to graph the line.

Explanation:

Step1: Find the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m=\frac{3}{4}\) (slope) and \(b = 2\) (y - intercept). When \(x = 0\), we substitute \(x = 0\) into the function \(f(x)=\frac{3}{4}x + 2\).
\(f(0)=\frac{3}{4}(0)+2=2\). So one point on the line is \((0,2)\).

Step2: Find another point using the slope

The slope \(m=\frac{3}{4}\) means that for a run (change in \(x\)) of \(4\), the rise (change in \(y\)) is \(3\). Starting from the point \((0,2)\), if we increase \(x\) by \(4\) (so \(x=0 + 4=4\)), we increase \(y\) by \(3\) (so \(y=2 + 3 = 5\)).
We can also verify by substituting \(x = 4\) into the function \(f(4)=\frac{3}{4}(4)+2=3 + 2=5\). So another point on the line is \((4,5)\).

To graph the line, we can use the two points \((0,2)\) and \((4,5)\) (or other points found using the slope - intercept form and slope) and draw a line through them using the line tool.

Answer:

To graph \(f(x)=\frac{3}{4}x + 2\), use the points \((0,2)\) (y - intercept) and \((4,5)\) (found using slope \(\frac{3}{4}\)) and draw a line through them with the line tool.