Chapter 4, Problem 4CR

To determine

The linear function having slope $-3$ passing through the point $\left(-1,4\right)$ and graph the function.

Answer to Problem 4CR

Solution:

The equation of the function is $f\left(x\right)=-3x+1$ and the graph is

  

Explanation of Solution

Given information:

The slope of the function is $-3$

The function passing through the point $\left(-1,4\right)$

The equation of the line passing through the point $\left(x_1,y_1\right)$ with slope $m$ is given as $y-y_1=m\left(x-x_1\right)$

Here, the slope is $m=-3$

Compare the given point $\left(-1,4\right)$ with $\left(x_1,y_1\right)$ , then $x_1=-1,y_1=4$

The function becomes

  $y-4=-3\left(x-\left(-1\right)\right)$

  $\Rightarrow y-4=-3\left(x+1\right)$

  $\Rightarrow y=-3x-3+4$

  $\Rightarrow y=-3x+1$

Replace $y$ by $f\left(x\right)$

Hence, the function is

  $f\left(x\right)=-3x+1$ .

To draw the graph of the function, plot the given point $\left(-1,4\right)$

Since the slope is $-3=\frac{-3}{1}=\frac{rise}{run}$ , move $3$ unit down and $1$ unit to the right.

This gives the point $\left(0,1\right)$ lies on the line

Draw the line through these two points.