Line g has an equation of y= – 2/9 x+6. Parallel to line g is line h, which passes through the point (3,2). What is the equation of line h?

Question

write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers

Answer 1

Hi Ari,

Because line h is parallel to line g, they must have the same slope, m = -2/9

Line h passes through point (3,2), so we can find the equation of the line by first using the point-slope form of the line equation, where (x_1,y₁) is (3,2). There is a faster way to do it but I like to use this definition (which itself is just the slope definition m = (y₂ - y₁) / (x₂ - x₁) rearranged and generalized for any point x₂,y₂) to show you where y = mx + b comes from instead of just memorizing it.

y - y₁ = m (x - x₂)

y - 2 = (-2/9) (x - 3)

Rearrange and multiply the slope into the parenthesis

y = (-2/9)x + 6/9 + 2

y = (-2/9)x + 24/9

y = (-2/9)x + 8/3