Question

1. graph the equation $y = 3x - 4$

Explanation:

Step1: Identify the slope-intercept form

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

Step2: Plot the y - intercept

The y - intercept is \( (0,-4) \). So we start by plotting the point \( (0,-4) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{3}{1}\) means that for every 1 unit we move to the right (increase in \( x \) by 1), we move up 3 units (increase in \( y \) by 3). Starting from \( (0,-4) \), if we move 1 unit to the right (to \( x = 1 \)) and 3 units up, we get the point \( (1,-4 + 3)=(1,-1) \). We can also move in the opposite direction: for a run of - 1 (move 1 unit to the left) and a rise of - 3 (move 3 units down) from \( (0,-4) \), we get the point \( (-1,-4-3)=(-1,-7) \).

Step4: Draw the line

After plotting two or more points (like \( (0,-4) \), \( (1,-1) \), \( (-1,-7) \)), we draw a straight line passing through these points. This line represents the graph of the equation \( y = 3x-4 \).

Answer:

The graph of \( y = 3x - 4 \) is a straight line with a y - intercept at \( (0,-4) \) and a slope of 3. It passes through points such as \( (0,-4) \), \( (1,-1) \), \( (-1,-7) \) (and other points found using the slope) and is drawn as a straight line connecting these points on the coordinate plane.