Question

A line goes through the points (-6, -8) and (12, 7). a) What is the slope of the line? Show your work. b) Write the equation of the line in point-slope form. Show your work c) Write the equation of the line in slope-intercept form. Show your work. Answer: a) b) c)

Answer 1

m = $\frac{5}{6}$ , y - 7 = $\frac{5}{6}$ ( x - 12), y = $\frac{5}{6}$ x - 3

(a) calculate the slope using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂) = (12, 7)

m = $\frac{7+8}{12+6}$ = $\frac{15}{18}$ = $\frac{5}{6}$

(b) the equation of a line in point-slope form is

y - b = m(x - a )

where m is the slope and (a, b) a point on the line

using m = $\frac{5}{6}$ and (a , b) = (12, 7 )

y - 7 = $\frac{5}{6}$ (x - 12)

(c) the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange (b ) into this form

y - 7 = $\frac{5}{6}$ - 10

y = $\frac{5}{6}$ x - 3