Q 23. - Precalculus Enhanced with Graphing Utilities

Question

Find an equation of the line having the given characteristics. Express your answer using either the general form or the

slope–intercept form of the equation of a line, whichever you prefer. Graph the line.

Containing the points $\left(3,-4\right)$ and $\left(2,1\right)$.

Step-by-Step Solution

Answer

Equation of the line is $y=-5x+11$. The graph of the equation is shown below.

Step 1. Given information.

Consider the given points $\left(3,-4\right)$ and $\left(2,1\right)$.

Step 2. Find the slope of line.

Substitute the values$x_1=3 ,y_1=-4$ and $x_2=2 ,y_2=1$ into the slope formula of the line $m=\frac{y_2-y_1}{x_2-x_1}$. 

$$\begin{gathered} m=\frac{1+4}{2-3} \\ m=-5 \end{gathered}$$

Further simplify to find the line passing through the two points.

Step 3. Find the slope intercept form of the equation.

Using formula to find line . 

$\left(y-y_1\right)=m\left(x-x_1\right)$

Substitute the value of $x_1, y_1$and m.

$$\begin{gathered} y+4=-5\left(x-3\right) \\ y=-5x+11 \end{gathered}$$

Step 4. Plot the graph.

The graph for the line $y=-5x+11$shown below.