Question

1. graph: $y = 4x - 3$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 4x - 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 4=\frac{4}{1} \) and \( b=-3 \).

Step2: Plot the y - intercept

The y - intercept is \( - 3 \), so we plot the point \( (0,-3) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{1} \) means we can go up 4 units and then right 1 unit from the point \( (0,-3) \). So from \( (0,-3) \), moving up 4 gives \( y=-3 + 4=1 \) and moving right 1 gives \( x = 0+1 = 1 \). So we get the point \( (1,1) \). We can also go down 4 units and left 1 unit from \( (0,-3) \) to get another point (for example, \( (-1,-7) \)), but two points are enough to draw a line.

Step4: Draw the line

Draw a straight line passing through the points \( (0,-3) \) and \( (1,1) \) (and other points we might have found).

Answer:

To graph \( y = 4x-3 \):

1. Plot the y - intercept at \( (0, - 3) \) (since when \( x = 0 \), \( y=4(0)-3=-3 \)).
2. Use the slope \( m = 4=\frac{4}{1} \): from \( (0,-3) \), move up 4 units and right 1 unit to get the point \( (1,1) \) (or other points using the slope).
3. Draw a straight line through the plotted points. The line should have a positive slope (going up from left to right) and cross the y - axis at \( (0,-3) \).