Algebra college

Question

Find the equation (in terms of x) of the line through the points (-2, -2) and (4, 5).

y=

Answer 1

Use two-point form:

(y - 2) / (x + 2) = (5 - 2) / (4 + 2)

Answer 2

Hi Krista,

You are probably very familiar with the general line equation y = mx + b, where m is the slope and b is the y-intercept of our line

Let's first write the slope of this line, which we can get by using the following equation: (x₁,y₁) and (x₂,y₂) are two given points that exist along this line. The problem gives us 2 such points: (-2, -2) and (4,5)

m = (y₂ - y₁) / (x₂ - x₁) = (5 - (-2)) / (4 - (-2)) = 7/6

Now, all we need is the y-intercept to write this equation in y = mx + b form. We could do this by graphing but let's do it using algebra to make sure we know how it works. Let's start by using the point-slope form equation for a line

y - y₁ = m (x - x₁)

(notice that the point-slope equation is just the slope definition, but rearranged by multiplying (x - x₁) term to both sides and generalizing x₂ to be the x-coordinate of any point on the line, x)

Plugging in what we know, this becomes

y - (-2) = (7/6) (x - (-2))

y + 2 = (7/6) (x +2)

Rearrange and multiply the 7/6 into the parenthesis

y = (7/6)x + 14/6 - 2 = (7/6)x + 14/6 - 12/6 = (7/6)x + 2/6 = (7/6)x + 1/3

y = (7/6)x + 1/3