In the standard (x, y) coordinate plane, a line passes through the points (-\frac{1}{2}, \… — ACT

In the standard $(x, y)$ coordinate plane, a line passes through the points $(-\frac{1}{2}, \frac{2}{3})$ and $(\frac{3}{4}, -\frac{1}{2})$ . What is the slope of this line?

A
$\frac{14}{15}$
B
$-\frac{15}{14}$
C
$-\frac{9}{10}$
$-\frac{14}{15}$ Answer
E
$-\frac{14}{3}$

Answer

The slope of the line is

-\frac{14}{15}

The slope of the line is found by using the slope formula

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

. Substituting the given points

(-\frac{1}{2}, \frac{2}{3})

and

(\frac{3}{4}, -\frac{1}{2})

into the formula, we find the change in

y

-\frac{7}{6}

and the change in

x

\frac{5}{4}

. Dividing the change in

y

by the change in

x

yields

-\frac{14}{15}

Step-by-Step Solution

Identify the coordinates of the two points as

(x_1, y_1) = (-\frac{1}{2}, \frac{2}{3})

and

(x_2, y_2) = (\frac{3}{4}, -\frac{1}{2})

x_1 = -\frac{1}{2}

y_1 = \frac{2}{3}

x_2 = \frac{3}{4}

, and

y_2 = -\frac{1}{2}

To use the slope formula, we must first map the given points to their respective coordinate variables.

Apply the slope formula

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

to calculate the change in

y

(rise) and the change in

x

(run).

Rise =

-\frac{1}{2} - \frac{2}{3} = -\frac{7}{6}

; Run = \frac{3}{4} - (-\frac{1}{2}) = \frac{5}{4}

The slope is the ratio of the vertical change to the horizontal change.

Divide the change in

y

by the change in

x

and simplify the resulting fraction.

m = \frac{-\frac{7}{6}}{\frac{5}{4}} = -\frac{7}{6} \times \frac{4}{5} = -\frac{28}{30} = -\frac{14}{15}

Dividing fractions is performed by multiplying the numerator fraction by the reciprocal of the denominator fraction.

Key Concept

Calculating the slope of a line between two points containing positive and negative fractional coordinates.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic