Question

Find the equation of line from the given graph:

Answer 1

Answer:

$y(x)=\frac{3}{4}x-\frac{18}{4}$

Explanation: We need to write the equation of the line which has the general form:

$y(x)=mx+b$

Where:

$\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ b=y-\text{intercept} \end{gathered}$

These two parameters are found as follows:

Slope:

$\begin{gathered} P_1(-2,-6) \\ P_2(2,-3) \\ \therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{-6-(-3)}{-2-2}=\frac{-3}{-4}=\frac{3}{4} \end{gathered}$

y-intercept:

From the graph, it is the point where the line intersects the y-axis, therefore it is:

$\begin{gathered} y(-2)=-6=\frac{3}{4}(-2)+b \\ \therefore\rightarrow \\ b=-6+\frac{6}{4}=\frac{-24+6}{4}=\frac{-18}{4}=-4.5 \end{gathered}$

And the graph agrees with it:

Equation of line is:

$y(x)=\frac{3}{4}x-\frac{18}{4}$