Answer :
Let's begin by listing out the information given to us:
[tex]\begin{gathered} (x_{1,}y_1)=(2,7) \\ (x_{2,}y_2)=(1,-4) \end{gathered}[/tex]Let's calculate the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-7}{1-2}=\frac{-11}{-1}=11[/tex]Slope = 11
Using point slope form, we have:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_2=m(x-x_2) \\ Using(1,-4) \\ y--4=11\left(x-1\right) \\ y+4=11x-11 \\ \text{Subtract 4 from both sides} \\ y=11x-15 \end{gathered}[/tex]Write the equation in slope intercept form, we have:
The general formula is given by y = mx + b
Let's calculate the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-7}{1-2}=\frac{-11}{-1}=11[/tex]The general formula becomes,
y = 11x + b
To solve for b, make b the subject formula, we have:
b = y - 11x
Substitute (2, 7) into the formula
b = 7 - 11 (2) = 7 - 22 = -15
b = -15
Substitute the value of b into the formula y = 11x + b, we have:
[tex]y=11x-15[/tex]