Question

graph $y = \frac{4}{5}x - 7$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{4}{5}x - 7 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{4}{5} \) (slope) and \( b = - 7 \) (y - intercept).

Step2: Plot the y-intercept

The y - intercept is \( (0,-7) \). Locate the point \( (0, - 7) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x} \). From the y - intercept \( (0,-7) \), move up 4 units (since the numerator of the slope is 4) and then move to the right 5 units (since the denominator of the slope is 5). This gives us the point \( (0 + 5,-7+4)=(5,-3) \). We can also move down 4 units and left 5 units from the y - intercept to get another point, for example, \( (0 - 5,-7 - 4)=(-5,-11) \).

Step4: Draw the line

Draw a straight line through the points that we have found (e.g., \( (0,-7) \) and \( (5,-3) \) or \( (0,-7) \) and \( (-5,-11) \)).

To graph the line correctly, we start by marking the y - intercept at \( (0,-7) \). Then, using the slope \( \frac{4}{5} \), from \( (0,-7) \), moving 5 units to the right (along the x - axis) and 4 units up (along the y - axis) gives the point \( (5,-3) \). Drawing a line through \( (0,-7) \) and \( (5,-3) \) (or other points found using the slope) will give the graph of \( y=\frac{4}{5}x - 7 \).

Answer:

The graph of \( y = \frac{4}{5}x-7 \) has a y - intercept at \( (0, - 7) \) and a slope of \( \frac{4}{5} \). Two points on the line can be \( (0,-7) \) and \( (5,-3) \), and a straight line is drawn through these points.