Explanation
Step 1
find the slope of the line
when you know 2 points of a line ( P1 and P2) , you can find the slope by using:
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_{_2},y_2) \end{gathered}[/tex]then, Let
P1(7,4)
P2(5,0)
replace,
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{0-4}{5-7} \\ \text{slope}=\frac{-4}{-2} \\ \text{slope}=2 \end{gathered}[/tex]Step 2
now, find the equation of the line
[tex]\begin{gathered} y-y_1=sl_{}ope(x-x_1) \\ \text{where} \\ P1(x_1,y_1)\text{ is a known point of the line} \end{gathered}[/tex]Let
P1(7,4)
now, replace
[tex]\begin{gathered} y-y_1=sl_{}ope(x-x_1) \\ y-4=2(x-7) \\ y-4=2x-14 \\ \text{add 4 in both sides} \\ y-4+4=2x-14+4 \\ y=2x-10 \end{gathered}[/tex]so, the answer is
[tex]y=2x-10[/tex]I hope this helps you
