In the standard (x, y) coordinate plane, a line passing through the points (-3, 5) and (1,… — ACT

In the standard $(x, y)$ coordinate plane, a line passing through the points $(-3, 5)$ and $(1, -3)$ has a slope of $-2$ . Is this statement true or false?

Answer: Answer

Answer

True

The statement is true because substituting the coordinates

(-3, 5)

and

(1, -3)

into the slope formula

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

yields

m = \frac{-3 - 5}{1 - (-3)} = \frac{-8}{4} = -2

, which exactly matches the stated slope value.

Step-by-Step Solution

Identify the coordinates of the two points on the line.

(x_1, y_1) = (-3, 5)

and

(x_2, y_2) = (1, -3)

The coordinates are needed to calculate the vertical change (rise) and horizontal change (run).

Apply the slope formula

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

m = \frac{-3 - 5}{1 - (-3)} = \frac{-8}{4} = -2

Subtracting

y_1

from

y_2

yields the change in

y

, and subtracting

x_1

from

x_2

yields the change in

x

. Subtracting a negative number becomes addition:

1 - (-3) = 1 + 3 = 4

Compare the calculated slope to the value stated in the problem.

The calculated slope is

-2

, which matches the given statement.

Since the calculated value agrees with the statement, the statement is true.

Key Concept

Slope of a Line

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic