<h3>y = 2x + 8 is the equation of line in slope intercept form</h3>
<em><u>Solution:</u></em>
Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14)
To find: Equation of the line in slope - intercept form
<h3><u>The equation of line in slope intercept form is:</u></h3>
y = mx + c ------ eqn 1
Where, "m" is the slope of line and "c" is the y intercept
<h3><u>Find the slope of line</u></h3>
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
From given,
![(x_1, y_1) = (-5, -2)\\\\(x_2, y_2) = (3, 14)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%28-5%2C%20-2%29%5C%5C%5C%5C%28x_2%2C%20y_2%29%20%3D%20%283%2C%2014%29)
Therefore,
![m = \frac{14-(-2)}{3-(-5)}\\\\m = \frac{14+2}{3+5}\\\\m = \frac{16}{8}\\\\m = 2](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B14-%28-2%29%7D%7B3-%28-5%29%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B14%2B2%7D%7B3%2B5%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B16%7D%7B8%7D%5C%5C%5C%5Cm%20%3D%202)
Thus slope of line is 2
<h3><u>Find the y intercept:</u></h3>
Substitute m = 2 and (x, y) = (-5, -2) in eqn 1
-2 = 2(-5) + c
-2 = -10 + c
c = -2 + 10
c = 8
<h3><u>Thus the equation of line is:</u></h3>
Substitute c = 8 and m = 2 in eqn 1
y = 2x + 8
Thus the equation of line is found