Question

this assessment has been due 2 weeks ago and i don't understand it

Answer 1

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:

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

The point slope formula:

$y-y_1=m(x-x_1)$

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

$\begin{gathered} y\text{ - }(-6)\text{ = 5(x - (-2))} \\ Point\text{ slope formula: }y\text{ +6 = 5(x + 2)} \end{gathered}$

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