Slope-intercept form is y = mx + b where m is the slope and b is the y-intercept. (the value of y when x = 0)
To find the slope, use the slope formula, [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where (x¹, y¹) and (x², y²) are your two points.
For (-2, 6) and (2, 14): [tex]m=\frac{14-6}{2-(-2)}=\frac{8}{2+2}=\frac84=2[/tex]
As a fraction, we would write the slope 2/1, but dividing by 1 is redundant when writing the actual equation.
Since slope is rise over run, we can interpret this slope as "when y changes by 2, x changes by 1 (and vice versa)"
Let's take one of our points, how about (-2, 6), and find our y-intercept from this.
We want to add 2 to x. According to our slope, this means adding 4 to y.
Our y-intercept is at (0, 10), with the value we put into our equation b = 10.
Final equation: y = 2x + 10
