Answer:
The equation of the line in standard form is:
[tex]6x + y = 62[/tex]
Step-by-step explanation:
Given the points
Determining the slope between (10, 2) and (14, -22)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(10,\:2\right),\:\left(x_2,\:y_2\right)=\left(14,\:-22\right)[/tex]
[tex]m=\frac{-22-2}{14-10}[/tex]
[tex]m=-6[/tex]
The point-slope form of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
substituting the values m = -6 and the point (10, 2) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 2 = -6(x - 10)[/tex]
[tex]y - 2 = -6x +60[/tex]
adding 2 to both sides
[tex]y-2+2 = -6x + 60 + 2[/tex]
[tex]y = -6x + 62[/tex]
We can write the equation in the standard form such as
Ax + By = C
Thus,
[tex]y = -6x + 62[/tex]
adding -6x to both sides
[tex]6x + y = -6x + 62 + -6x[/tex]
[tex]6x + y = 62[/tex]
Therefore, the equation of the line in standard form is:
[tex]6x + y = 62[/tex]
