i) m =5
ii) y +6 = 5(x + 2)
iii) y = 5x +4
Explanation:
The points on your work: (-2, -6) and (1, 9)
we apply the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=-2,y_1=-6,x_2=1,y_2\text{ = }9 \\ m\text{ = }\frac{9-(-6)}{1-(-2)}=\frac{9+6}{1+2}=\frac{15}{3} \\ m\text{ = 5} \end{gathered}[/tex]
The point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
we can use any of the points given for x1 and y1. Let's go with the one used above where x1 = -2 and y1 = -6
[tex]\begin{gathered} y\text{ - }(-6)\text{ = 5(x - (-2))} \\ Point\text{ slope formula: }y\text{ +6 = 5(x + 2)} \end{gathered}[/tex]
Slope intercept form:
y = mx + c
we need to find c which is the y-intercept
using any points above: (-2, -6) = (x, y)
Insert the point into the formula as (x, y) to get c
-6 = 5(-2) + c
-6 = -10 + c
-6+10 = c
c = 4
Slope intercept form: y = 5x + 4
