Question

Write an equation in slope-intercept form of the line that passes through the points (2, 4) and (3,6).

Answer 1

`y=2x`

Explanation:

We want to write an equation in slope-intercept form that passes through the points (2, 4) and (3, 6).

So, we will first find the slope. Let (2, 4) be (x₁, y₁) an let (3, 6) be (x₂, y₂).

The slope formula is given by:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

So, by substitution, our slope is:

`\displaystyle m=(6-4)/(3-2)=(2)/(1)=2`

Now, we can use the point-slope form:

`y-y_1=m(x-x_1)`

By substitution:

`y-(4)=2(x-(2))`

Distribute:

`y-4=2x-4`

Adding 4 to both sides yields:

`y=2x`

And we have our equation.

In this case, the y-intercept is 0.