Question

4 sketch the graph of each line: $y = \frac{3}{5}x - 4$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{3}{5}x - 4 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{3}{5} \) (slope) and \( b=- 4 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept is \( b=-4 \), so we plot the point \( (0,-4) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m = \frac{3}{5}\) means "rise over run", that is, for a run (change in x) of 5 units, the rise (change in y) is 3 units. Starting from the point \( (0,-4) \), if we move 5 units to the right (increase x by 5) and 3 units up (increase y by 3), we get the point \( (0 + 5,-4+3)=(5,-1) \).

Step4: Draw the line

Draw a straight line passing through the points \( (0,-4) \) and \( (5,-1) \).

Answer:

To sketch the graph of \( y=\frac{3}{5}x - 4 \):

1. Plot the y - intercept \( (0,-4) \).
2. Use the slope \( \frac{3}{5} \) to find another point (e.g., from \( (0,-4) \), move 5 units right and 3 units up to get \( (5,-1) \)).
3. Draw a straight line through these two points.