Question

graph the line with the equation $y = \frac{3}{5}x - 4$.

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m=\frac{3}{5}\) (slope) and \(b = - 4\) (y - intercept). So, the line crosses the y - axis at \((0,-4)\).

Step2: Use the slope to find another point

The slope \(m=\frac{3}{5}\) means for every 5 units we move to the right (increase in \(x\) by 5), we move up 3 units (increase in \(y\) by 3). Starting from \((0,-4)\), if we move \(x = 5\), then \(y=\frac{3}{5}(5)-4=3 - 4=-1\). So, another point on the line is \((5,-1)\).

Step3: Plot the points and draw the line

Plot the points \((0,-4)\) and \((5,-1)\) on the coordinate plane. Then, draw a straight line passing through these two points.

Answer:

The line is graphed by plotting the y - intercept \((0, - 4)\) and using the slope \(\frac{3}{5}\) to find another point \((5,-1)\) (or other points using the slope) and then drawing a line through the plotted points. (Note: Since the task is to graph, the final answer is the graph with points \((0,-4)\), \((5,-1)\) (and others) connected by a straight line.)