Question

16. Calculate the slope of the line that passes through the two points (-4,2) and (1,3).
17. Calculate the slope of the line that passes through the two points (-1,-2) and (2,7).
18. Identify the slope and y intercept of the following equation. 4y=x+8
19. Identify the slope and y intercept of the following equation. 3x+9y=56
If you can please show your work

Answer 1

Question 16

(-4 , 2) (1 , 3)

$slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Insert values into formula

$slope=\frac{3-2}{1-(-4)}$

$slope=\frac{1}{5}$

Answer: slope = 1/5 or 0.2

Question 17

(-1 , -2) (2 , 7)

$slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Insert values into formula

$slope=\frac{7-(-2)}{2-(-1)}$

$slope=\frac{9}{3}$

$slope=3$

Answer: slope = 3

Question 18

$4y=x+8$

Divide each term in the equation by 4 to get it into the form $y=mx+c$ where m=slope and c=y intercept

$4y/4=x/4+8/4$

$y=\frac{1}{4} x+2$

Now that the equation is in the form $y=mx+c$ the slope and y intercept can be identified.

slope = 1/4

y intercept = 2

Answer: slope = 1/4 and y intercept = 2

Question 19

$3x+9y=56$

We have to rearrange the equation into the form $y=mx+c$ where m=slope and c=y intercept

$9y=-3x+56$

Divide each term in the equation by 9 to get it into the form $y=mx+c$ where m=slope and c=y intercept

$9y/9=-3x/9+56/9$

$y=-\frac{1}{3}x+\frac{56}{9}$

Now that the equation is in the form $y=mx+c$ the slope and y intercept can be identified.

slope = $-\frac{1}{3}$

y intercept = 56/9

Answer: slope = $-\frac{1}{3}$ and y intercept = 54/9