On a coordinate map of a state park, a straight hiking trail begins at a campsite located … — ACT

On a coordinate map of a state park, a straight hiking trail begins at a campsite located at $(2, -3)$ and ends at a lookout point. A hiker walks along the trail at a constant pace, and after $3$ hours, reaches a trail marker located at $(11, 9)$ . What is the slope of the line on the coordinate map that represents this straight trail?

$\frac{4}{3}$ Answer
B
$\frac{3}{4}$
C
$\frac{2}{3}$
D
$-\frac{4}{3}$
E
$5$

Answer

\frac{4}{3}

To find the slope of the line representing the trail, we identify the two points through which the line passes:

(2, -3)

and

(11, 9)

. Applying the slope formula

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

, we get

m = \frac{9 - (-3)}{11 - 2} = \frac{12}{9}

. Simplifying the fraction by dividing the numerator and denominator by

3

yields the correct slope of

\frac{4}{3}

Step-by-Step Solution

Identify the coordinates of the two points on the line representing the trail.

The two points are the campsite at

(2, -3)

and the trail marker at

(11, 9)

To find the slope of a straight line, we need the coordinates of any two points that lie on the line.

Set up the slope formula.

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

The slope of a line is defined as the change in the

y

-coordinates (rise) divided by the change in the

x

-coordinates (run).

Substitute the coordinate values into the formula and simplify.

m = \frac{9 - (-3)}{11 - 2} = \frac{9 + 3}{9} = \frac{12}{9}

Substituting the coordinates correctly handles the subtraction of the negative coordinate.

Reduce the fraction to simplest form.

m = \frac{4}{3}

Dividing the numerator and the denominator by their greatest common divisor,

3

, yields the final simplified slope value.

Key Concept

Calculating the slope of a line given two points on a coordinate plane

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic