Question

What is the equation of the line graphed below?

Express your answer in point-slope form using the point $\left(-8,3\right)$.

Short answer

The required equation is represented by$\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{1}}{\mathbf{4}}\mathit{x}\mathbf{+}\mathbf{1}$.

Step-by-step solution

Step 1. Determine the formula that can be used.

The standard form associated with a line that is having travel through points which are two in the 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 point and the point which represents the traveling of the line through the horizontal axis $\left(4,0\right)$as they are in the form of $\left(x_1,y_1\right),\left(x_2,y_2\right)$.

$$\begin{gathered} y-0=\frac{3-0}{-8-4}\left(x-4\right) \\ y=-\frac{1}{4}x+1 \end{gathered}$$

Step 3. Write the conclusion. 

The obtained equation is$y=-\frac{1}{4}x+1$ so is the required equation.