Question

How do you write an equation of a line that passes through (4,3) and has a slope of 2?

Answer 1

`y = 2x-5`, see below.

Explanation:

There is enough information to make a point slope equation that we can later convert into slope intercept.

Point slope form is:

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

`(x_1,y_1): \text{A point.} \\\\m - \text{Slope.}`

We are given the slope of 2 and the point (4,3).

Replace the variables with the given information.

`y-y_1=m(x-x_1)\rightarrow y-3=2(x-4)`

With the equation we will now convert it into slope intercept form:

`y-3=2(x-4)\\\\y-3=2x-8\\\\y-3+3=2x-8+3\\\\\boxed{y=2x-5}`

Hope this helps!

Answer 2

y = 2x - 5

Explanation:

y-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We know the slope is 2, so all that's left is to find the y-intercept. To do this, for every 1 we subtract from x in (4,3), we take away 2 from y because the slope is two. We keep doing this until x is zero. The remaining y-value is the y-intercept.