Question

graph the following linear equation.
y = 4x + 3

use the graphing tool to graph the linear equation.
click to enlarge graph

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, \( m = 4 \) (which can be written as \( \frac{4}{1} \)) 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 that from the point \( (0,3) \), we move up 4 units (because the numerator of the slope is 4, which represents the rise) and then move 1 unit to the right (because the denominator of the slope is 1, which represents the run). So from \( (0,3) \), moving up 4 units and right 1 unit gives us the point \( (0 + 1,3+4)=(1,7) \). We can also move down 4 units and left 1 unit from \( (0,3) \) to get another point \( (0 - 1,3-4)=(- 1,-1) \).

Step4: Draw the line

After plotting at least two points (e.g., \( (0,3) \) and \( (1,7) \) or \( (0,3) \) and \( (-1,-1) \)), we draw a straight line passing through these points. This line represents the graph of the linear equation \( y = 4x+3 \).

(Note: Since the problem mentions using a graphing tool, the actual graphing would be done on the provided graphing interface by marking the y - intercept and then using the slope to find additional points and drawing the line. The key steps above are for understanding how to graph the line.)

Answer:

The graph of \( y = 4x + 3 \) is a straight line with a y - intercept at \( (0,3) \) and a slope of 4. When using the graphing tool, plot \( (0,3) \), then use the slope to find another point (e.g., \( (1,7) \)) and draw the line through these points.