Question

Write an equation of the line in slope-intercept form that passes through the given points.

$\left(2,5\right)$,$\left(-2,8\right)$

Short answer

The required equation is represented by $y=\frac{-3}{4}x+3$.

Step-by-step solution

Step 1. Determine the formula that can be used.

The standard form associated with line that is having a travel through points which are two in count$y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ can be used to calculate the required equation.

Step 2. Take the help of the obtained method.

Take the help of obtained standard form represented by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$in which the required values can be filled by using the provided points as they are in the form of $\left(x_1,y_1\right)$$\left(x_2,y_2\right)$.

role="math" localid="1647430232281" $$\begin{gathered} y-5=\frac{8-5}{\left(-2\right)-2}\left(x-2\right) \\ y-5=-\frac{3}{4}\left(x-2\right) \\ y=\frac{-3}{4}x-2+5 \\ y=\frac{-3}{4}x+3 \end{gathered}$$

Step 3. Write the conclusion.

The obtained equation is$y=-\frac{3}{4}x+3$so it is the required equation.