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$\left(2,1\right)$.

Short answer

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

Step-by-step solution

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.