Question

Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)

(2, 6) and (4, 16)

Answer 1

Let's find the eqn. of this line in slope-intercept form, y = mx + b.
The two constants in the equation we need are the slope m and y-intercept b.

We can find the slope using "rise over run."
$m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{16-6}{4-2}=\frac{10}2=5$

We can interpret this slope in its fraction form 5/1 being rise over run as
"If y changes by 5, x changes by 1, and vice versa."

We can use this to find our y-intercept. (the value of y when x = 0)
Take our point (2, 6). We want to subtract 2 from x so that x = 0.
According to our slope, this means subtracting 10 from y.
Our y-intercept would be at (0, -4), with the value we put in our eqn. being -4.

$\boxed{y=5x-4}$