Question

Y equals equation for the line that passes through the points (-6,2) and (1,16)

Answer 1

Slope-intercept form:  y = mx + b  

[m is the slope, b is the y-intercept or the y value when x = 0  --->  (0, y)  or the point where the line crosses through the y-axis]

To find the slope, you use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$       And plug in the two points

(-6, 2)  =  (x₁ , y₁)

(1, 16)  =  (x₂ , y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{16-2}{1-(-6)}$     [two negatives cancel each other out and become positive]

$m=\frac{16-2}{1+6}$

$m=\frac{14}{7}$

m = 2       Now that you found m, plug it into the equation

y = mx + b

y = 2x + b        To find b, plug in one of the points into the equation

(-6, 2)

y = 2x + b

2 = 2(-6) + b

2 = -12 + b          Add 12 on both sides

14 = b

(1, 16)

y = 2x + b

16 = 2(1) + b          Subtract 2 on both sides

14 = b        

Now that you found b, plug it into the equation

y = 2x + 14