Question

Plot the function given by the following equation and identify the intercepts.

f(x)=23x+6

Answer 1

To plot the function f(x)=23x+6, we need to identify the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.

Comparing the given function f(x)=23x+6 to the slope-intercept form, we can see that the slope, m, is 23 and the y-intercept, b, is 6.

Plotting the function
To plot the function, we start by identifying the y-intercept. The y-intercept occurs when x=0. Substituting x=0 into the function, we get:
f(0) = 23(0) + 6
f(0) = 6

So, the y-intercept is (0, 6).

Next, we can find another point on the line by using the slope. The slope m=23 can be expressed as a ratio of rise to run. Here, the rise is 23 (change in y) and the run is 1 (change in x).

Starting from the y-intercept (0, 6), we can move 23 units up and 1 unit to the right to find the next point. This gives us the point (1, 29).

Plotting these two points and drawing a straight line passing through them, we get the graph of the function f(x)=23x+6.

The intercepts:
- The y-intercept is (0, 6).
- There is no x-intercept since the function is a linear equation with positive slope. This means that the line intersects the x-axis at a point to the left of the y-axis, which is not within the range of the given equation.