Given
[tex]\begin{gathered} P(0,-4) \\ Q(5,1) \end{gathered}[/tex]
Solution
Step 1
Find the slope
Formula
[tex]\begin{gathered} \text{Slope (M)=}\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]
Given
[tex]\begin{gathered} x_1=0_{} \\ x_2=\text{ 5} \\ y_1=\text{ -4} \\ y_2=\text{ 1} \end{gathered}[/tex]
[tex]\text{Slope (M)=}\frac{1-(-4)}{5-0}=\frac{5}{5}=1[/tex]
Step 2
Find the equation of a line
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}[/tex]
We can choose any point either P or Q
[tex]\begin{gathered} P(0,-4) \\ x_1=0 \\ y_1=-4 \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=1(x-0) \\ y+4=x \\ y=x-4 \end{gathered}[/tex]
The final answer
[tex]y=x-4[/tex]
