Question

Solve the following question in the photo

Answer 1

y = 2x + 2

Explanation:

(6,14) and (10,22)

14 - 22= -8

6 - 10 = -4

-8/-4= 2

2 is slope

Y = 2x + B

Let’s find B

Use one of the coordinates

14= 2 x 6 + B

14 = 12 + B

Subtract 12 from both sides

2 = B

So B = 2

Y = 2x + 2

Answer 2

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

`(\stackrel{x_1}{10}~,~\stackrel{y_1}{22})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{42}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{42}-\stackrel{y1}{22}}}{\underset{\textit{\large run}} {\underset{x_2}{20}-\underset{x_1}{10}}} \implies \cfrac{ 20 }{ 10 } \implies \text{\LARGE 2}`