Graph from slope-intercept form Graph y=4x−9.
The Correct Answer and Explanation is:
Of course. Here is an explanation of how to graph the linear equation provided.
Graphing the Equation y = 4x – 9
The given equation, y = 4x – 9, is presented in the slope-intercept form, which is written as y = mx + b. This form is particularly useful for graphing because it directly provides two key pieces of information about the line: its slope (m) and its y-intercept (b).
Step 1: Identify the y-intercept (b)
The y-intercept is the point where the line crosses the vertical y-axis. In the general form y = mx + b, the ‘b’ value represents the y-coordinate of this intercept. For the equation y = 4x – 9, the value of b is -9.
This means the line passes through the point on the y-axis where y = -9. The coordinates for the y-intercept are therefore (0, -9). To begin graphing, this point is plotted on the coordinate plane.
Step 2: Identify the slope (m)
The slope of a line describes its steepness and direction. In the equation y = mx + b, the ‘m’ value represents the slope. For the equation y = 4x – 9, the slope m is 4.
The slope is often thought of as “rise over run” (the change in y divided by the change in x). A whole number like 4 can be written as a fraction to make this relationship clear: m = 4/1.
- Rise = 4: This indicates a vertical change of 4 units upwards.
- Run = 1: This indicates a horizontal change of 1 unit to the right.
Step 3: Use the slope to find a second point
Starting from the y-intercept (0, -9), the slope is used to find another point on the line.
- From the point (0, -9), move up 4 units (the rise). This brings you to y = -5.
- From that new position, move to the right 1 unit (the run). This brings you to x = 1.
The coordinates of the second point are (1, -5). This process can be repeated from the new point to find more points. For example, starting from (1, -5), rising 4 and running 1 leads to the point (2, -1).
Step 4: Draw the Line
Once at least two points, such as (0, -9) and (1, -5), are plotted on the graph, a straight line is drawn passing through them. This line extends indefinitely in both directions and represents all the coordinate pairs (x, y) that are solutions to the equation y = 4x – 9. The graph provided in the image correctly illustrates this line, passing through the y-intercept at -9 and rising steeply with a slope of 4.
