Questions: Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points is increasing, decreasing, horizontal, or vertical. (-8, -5) and (7, 3) A. 1/3 rises B. -8/15 falls C. 1/2 falls D. 8/15 rises

Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points is increasing, decreasing, horizontal, or vertical. (-8, -5) and (7, 3) A. 1/3 rises B. -8/15 falls C. 1/2 falls D. 8/15 rises
Transcript text: MA 0800 - 01 Intermediate Algebra Quiz: Quiz 4 (2.1, 2.2, 2.3) Question 4 of 7 Question list Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points is increasing, decreasing, horizontal, or vertical. (-8, -5) and (7, 3) A. $\frac{1}{3}$ rises B. -$\frac{8}{15}$ falls C. $\frac{1}{2}$ falls D. $\frac{8}{15}$ rises
failed

Solution

failed
failed

Solution Steps

To find the slope of the line through two points, use the formula for the slope \( m \) which is \((y_2 - y_1) / (x_2 - x_1)\). Substitute the given points into this formula to calculate the slope. Once the slope is determined, analyze its sign: a positive slope indicates the line is increasing (rises), a negative slope indicates the line is decreasing (falls), a zero slope indicates a horizontal line, and an undefined slope (division by zero) indicates a vertical line.

Step 1: Calculate the Slope

To find the slope \( m \) of the line through the points \((-8, -5)\) and \( (7, 3) \), use the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-5)}{7 - (-8)} = \frac{3 + 5}{7 + 8} = \frac{8}{15} \]

Step 2: Determine the Nature of the Line

The slope \( m = \frac{8}{15} \) is positive, which indicates that the line is increasing. Therefore, the line through the points \((-8, -5)\) and \( (7, 3) \) rises.

Final Answer

The slope of the line is \(\frac{8}{15}\) and the line rises. Therefore, the answer is \(\boxed{D}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Select all the organisms that are members of domain Eukarya. More than one option may be correct. multicellular protists bacteria archaea fungi animals unicellular protists plants
failedAnswered
Explain how an individual's phenotype may be determined by multiple genes that interact with one another and with the environment. Tongue rolling was thought to be an example of a human trait controlled by a single gene, but we now know that identical twins, who share 100% of their DNA sequences, will only share the tongue-rolling trait 70% of the time. This indicates that tongue rolling may also be controlled by the environment.
failedAnswered
Skip Which of the following is an allusion? Asking her personal questions is like opening Pandora's box. Aidan eats every meal like it is his last. Her eyes are as blue as the sky.
failedAnswered
∫ dx / (x^2 + 2x + 26)
failedAnswered
Question 5 of 24 This test 24 point(s) possible This question: 1 point(s) possible Submit 1 Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=x^3-8x^2-31x-22 Find the real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. x= (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma separate answers as needed.) B. There are no real zeros. Use the real zeros to factor f. f(x)= (Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)