write the equation of the line that passes through the points (2, -8) and (-1, 4). put your answer in fully…
write the equation of the line that passes through the points (2, -8) and (-1, 4). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.
Answer
Explanation:
Step1: Calculate the slope
The slope ( m ) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Here, ((x_1, y_1)=(2, - 8)) and ((x_2, y_2)=(-1,4)). So ( m=\frac{4 - (-8)}{-1 - 2}=\frac{12}{-3}=-4 ).
Step2: Use point - slope form
The point - slope form of a line is ( y - y_1=m(x - x_1) ). We can use the point ((2,-8)) (we could also use ((-1,4))). Substitute ( m=-4 ), ( x_1 = 2 ) and ( y_1=-8 ) into the formula: ( y-(-8)=-4(x - 2) ), which simplifies to ( y + 8=-4(x - 2) ).