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algebra 1 semester a test - part 1
graph the function.
$f(x) = \frac{3}{5}x - 5$
use the line tool and select two points to graph.
move line undo redo reset
10 y
9

Explanation:

Step1: Find the y-intercept

The function is in slope - intercept form \(y = mx + b\), where \(m=\frac{3}{5}\) (slope) and \(b = - 5\) (y - intercept). When \(x = 0\), \(f(0)=\frac{3}{5}(0)-5=-5\). So one point is \((0,-5)\).

Step2: Find another point using the slope

The slope \(m=\frac{3}{5}\) means for a run of \(5\) (change in \(x\)), the rise is \(3\) (change in \(y\)). Starting from \((0,-5)\), if we add \(5\) to \(x\) (so \(x = 0 + 5=5\)) and add \(3\) to \(y\) (so \(y=-5 + 3=-2\)), we get the point \((5,-2)\). We can also use \(x = 5\) in the function: \(f(5)=\frac{3}{5}(5)-5=3 - 5=-2\), which confirms the point \((5,-2)\).
To graph the line, we use the Line tool and plot the points \((0,-5)\) and \((5,-2)\) (or other points found using the slope - intercept form and slope properties) and draw the line through them.

Answer:

To graph \(f(x)=\frac{3}{5}x - 5\), plot the points \((0,-5)\) (y - intercept) and \((5,-2)\) (using slope \(\frac{3}{5}\) from \((0,-5)\)) and draw a line through them using the Line tool.