Question

1. what is the slope of ( overline{tv} ) if the point ( t ) is ( (2, -3) ) and the point ( v ) is ( (-1, -4) )?

a. ( -3 )
b. ( -\frac{1}{3} )
c. ( \frac{1}{3} )
d. ( 3 )

1. which of the following is the slope of the line represented by the equation ( 5y - 2x = 18 )?

a. ( -\frac{5}{2} )
b. ( -\frac{2}{5} )
c. ( \frac{2}{5} )
d. ( \frac{5}{2} )

Explanation:

(Problem 4):

Step1: Recall slope formula

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

Step2: Assign coordinate values

Let $(x_1,y_1)=(2,-3)$, $(x_2,y_2)=(-1,-4)$

Step3: Substitute into formula

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

(Problem 5):

Step1: Rearrange to slope-intercept form

Slope-intercept form: $y=mx+b$

Step2: Isolate $y$ term

$5y = 2x + 18$

Step3: Solve for $y$

$y = \frac{2}{5}x + \frac{18}{5}$, so slope $m=\frac{2}{5}$

Answer:

1. C. $\frac{1}{3}$
2. C. $\frac{2}{5}$