MATH SOLVE

4 months ago

Q:
# Determine the slope for the line that meets each condition stated. Show your work.a.Passes through the points (3,5) and (−1,−7).b.Passes through the points given by the table of values.x y−2 −7−1 −60 −51 −42 −3

Accepted Solution

A:

Answer: a. The slope is 3 b. The slope is 1Step-by-step explanation: We can calculate the slope of a line with the following formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] a. Knowing that the line passes through the points (3,5) and (-1,-7), we can identify that: [tex]y_2=-7\\y_1=5\\\\x_2=-1\\x_1=3[/tex] Then, substituting values into the formula, we get that the slope of this line is: [tex]m=\frac{-7-5}{-1-3}\\\\m=\frac{-12}{-4}\\\\m=3[/tex] b. Choose two points from the table. Let's choose: [tex](-2,-7)\\\\(2,-3)[/tex] In this case: [tex]y_2=-7\\y_1=-3\\\\x_2=-2\\x_1=2[/tex] Then, substituting values into the formula, we get that the slope of this line is: [tex]m=\frac{-7-(-3)}{-2-2}\\\\m=\frac{-4}{-4}\\\\m=1[/tex]