Question

A line passes through (3, –2) and (8, 2).

a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.

a. y – 2 = 4/5(x – 3); –4x + 5y = 22
b. y + 2 = 4/5(x + 3); –4x + 5y = –22
c. y – 3 = 4/5(x + 2); –4x + 5y = 23
d. y + 2 = 4/5(x - 3); -4x + 5y = -22

Answer 1

The point-slope form:

`y-y_1=m(x-x_1)`
m - slope
(x₁,y₁) - point


`(3,-2) \\ x_1=3 \\ y_1=-2 \\ \\ (8,2) \\ x_2=8 \\ y_2=2 \\ \\ \hbox{the slope:} \\ m=(y_2-y_1)/(x_2-x_1)=(2-(-2))/(8-3)=(2+2)/(5)=(4)/(5) \\ \\ \hbox{the point-slope form:} \\ y-y_1=m(x-x_1) \\ y-(-2)=(4)/(5)(x-3) \\ \boxed{y+2=(4)/(5)(x-3)}`


`\hbox{the standard form:} \\ y+2=(4)/(5)(x-3) \\ y+2=(4)/(5)x-(12)/(5) \\ -(4)/(5)x+y=-(12)/(5)-2 \ \ \ |* 5 \\ -4x+5y=-12-10 \\ \boxed{-4x+5y=-22}`

The answer is D.