Question

graph this line using the slope and y - intercept:
y = \frac{4}{5}x - 6
click to select points on the graph.

Explanation:

Step1: Identify the \(y\)-intercept

The equation of the line is in the slope - intercept form \(y=mx + b\), where \(b\) is the \(y\)-intercept. For \(y=\frac{4}{5}x-6\), \(b=-6\). So, one point on the line is \((0,-6)\).

Step2: Use the slope to find another point

The slope \(m = \frac{4}{5}\). Starting from the \(y\)-intercept \((0,-6)\), if we move \(x\) by \(\Delta x=5\) (denominator of the slope), then \(y\) changes by \(\Delta y = 4\) (numerator of the slope). Using the formula \(y_2=y_1+\Delta y\) and \(x_2=x_1+\Delta x\), with \(x_1 = 0,y_1=-6,\Delta x = 5,\Delta y=4\), we get \(x_2=0 + 5=5\) and \(y_2=-6+4=-2\). So, another point is \((5,-2)\).

Step3: Draw the line

Plot the points \((0,-6)\) and \((5,-2)\) on the coordinate plane and draw a straight line passing through them. This line represents the equation \(y=\frac{4}{5}x-6\).

Answer:

To graph the line \( y=\frac{4}{5}x - 6\), first plot the \(y\)-intercept \((0,-6)\). Then, using the slope \(\frac{4}{5}\) (which means for every 5 units we move to the right along the \(x\)-axis, we move 4 units up along the \(y\)-axis), from the point \((0,-6)\), move 5 units to the right (to \(x = 5\)) and 4 units up (to \(y=-6 + 4=-2\)), so we get the point \((5,-2)\). Connect these two points to draw the line.