Question

What is the equation of the line passing through `(4,5), (5,7)`?

Answer 1

Slope-intercept form: `y=2x-3`

Explanation:

Given two points, we can calculate the slope using the formula `m = \frac (y_2-y_1)(x_2-x_1)`.

So, `m = \frac (7-5)(5-4)`, which simplifies to `\frac2 1`, or just `2`.

Knowing this, we can substitute numbers into slope-intercept form (`y=mx+b`). Either point will work for this, but I used the first one just because:

`5=2(4)+b`

Now we simplify:
`5=8+b`

Subtract 8 from both sides to isolate b:
`-3=b`

Now that we have the y-intercept, we can write the equation:
`y=2x-3`.