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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)

1 Answer

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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=(rise)/(run)=(y_2-y_1)/(x_2-x_1)=(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}
User Afkbowflexin
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