Question

Write an equation for the line graphed

Answer 1

Answer:

y = 3x + 2

Step-by-step explanation:

So we can use the point-slope equation to help us figure out our y = mx +b equation

First we need to choose two points on the graph so we can calculate our slope

I personally like to choose point that intersects two numbers perfectly on the line rather than a point that is maybe half way between two numbers

So we can use the point (0,2) and the point (2,8)

Our (0,2) will represent (x₁, y₁) and our (2,8) will represent (x₂,y₂)

The equation to find the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }$, so plugging in our values, we get $m=\frac{8-2}{2-0} =\frac{6}{2} =3$

We have found our slope, 3, and now we can use the point-slope equation: y - y₁ = m(x - x₁) to figure out the remainder of the equation.

Plugging in our values we get: y - (2) = (3)(x - (0)) which simplifies to y - 2 = 3x which then simplifies to y = 3x + 2