A line passes through the points ( – 8, – 9) and ( – 10, – 10). What is its equation in point-slope form?

Answer 1

Point-slope form looks like...

y - y₁ = m(x - x₁)

To find m, the slope, we do difference in y/difference in x.

m = (-10 - (-9))/(-10 - (-8)) = (-10 + 9)/(-10 + 8) = -1/-2 = 1/2

y - (-9) = 1/2(x - (-8))

y + 9 = 1/2(x + 8)

Answer 2

Point-slope form is one of the more commonly used forms of a linear equation, and has the following structure:

y - y₁ = m(x - x₁)

The slope, m, is "rise over run": m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( (-10) - (-9) ) / ( (-10) - (-8) )

m = -1 / -2

m = 1/2

So, the point slope form of the equation is:

y - (-9) = (1/2)( x - (-8) )

y + 9 = (1/2)(x+8)

Answer 3

(-8, -9) & (-10, -10) have a line through them with slope = "rise over run" = difference in y values divided by difference in x values = (-9+10)/(-8+10) = 1/2

(y+10) = (1/2)(x+10)

y = (1/2)x +5 -10

y = (1/2)x - 5 in slope intercept form

or

2y + 20 = x+10

x-2y = 10 in general form

point slope form can use either point

y+10 = (1/2)(x+10) using the point (-10, -10)

or

y +9 = (1/2)(x+ 8) using the point (-8, -9)