### Finding the Equation for a Linear FunctionTo determine the equation of a linear function that passes through the given points (-4, 10) and (8, -5), follow these steps:#### a. Plotting the PointsUse the grid provided to plot the points:1. Locate point (-4, 10). This point is found by moving 4 units to the left along the x-axis (negative direction) and then moving 10 units up along the y-axis.2. Locate point (8, -5). This point is found by moving 8 units to the right along the x-axis (positive direction) and then moving 5 units down along the y-axis.#### b. Calculating the SlopeTo find the slope (m) between the two points, use the formula:\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]Substitute the values from the points (-4, 10) and (8, -5):\[ m = \frac{-5 - 10}{8 - (-4)} \]\[ m = \frac{-15}{12} \]\[ m = \frac{-5}{4} \]The slope between the points is $-\frac{5}{4}$.#### c. Determining the y-InterceptTo find the y-intercept (b), use the equation of the line $y = mx + b$. Substitute one of the points and the calculated slope into the equation:Using point (-4, 10):\[ 10 = -\frac{5}{4}(-4) + b \]\[ 10 = 5 + b \]\[ b = 5 \]The y-intercept is 5.#### d. Writing the Linear FunctionCombine the slope and y-intercept to write the equation of the line:\[ y = -\frac{5}{4}x + 5 \]This is the equation of the linear function passing through the points (-4, 10) and (8, -5).### Diagram ExplanationThe provided grid is an empty coordinate plane with both the x-axis and y-axis ranging from -10 to 10. The tool allows plotting and drawing lines to visualize the points and the resulting linear function.

Answered: Image /qna-images/answer/78eefbca-465a-4d0b-8c33-547a8a5c4c72.jpg

Find the equation for the linear function that passes through the points (- 4, 10) and (8, – 5). Answers must use whole numbers and/or fractions, not decimals. a. Use the line tool below to plot the two points. 10 9- 7- 2- -11 -10 -9 -8 -7 -6 -5 -4 -2 8 9 10 il -2 -4 -7 -8 9 10 Clear All Draw: b. State the slope between the points as a reduced fraction. c. State the y-intercept of the linear function. d. State the linear function.

Find the equation for the linear function that passes through the points (- 4, 10) and (8, – 5). Answers must use whole numbers and/or fractions, not decimals. a. Use the line tool below to plot the two points. 10 9- 7- 2- -11 -10 -9 -8 -7 -6 -5 -4 -2 8 9 10 il -2 -4 -7 -8 9 10 Clear All Draw: b. State the slope between the points as a reduced fraction. c. State the y-intercept of the linear function. d. State the linear function.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

### Finding the Equation for a Linear Function

To determine the equation of a linear function that passes through the given points (-4, 10) and (8, -5), follow these steps:

#### a. Plotting the Points
Use the grid provided to plot the points:

1. Locate point (-4, 10). This point is found by moving 4 units to the left along the x-axis (negative direction) and then moving 10 units up along the y-axis.
2. Locate point (8, -5). This point is found by moving 8 units to the right along the x-axis (positive direction) and then moving 5 units down along the y-axis.

#### b. Calculating the Slope
To find the slope (m) between the two points, use the formula:

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

Substitute the values from the points (-4, 10) and (8, -5):

\[ m = \frac{-5 - 10}{8 - (-4)} \]
\[ m = \frac{-15}{12} \]
\[ m = \frac{-5}{4} \]

The slope between the points is $-\frac{5}{4}$.

#### c. Determining the y-Intercept
To find the y-intercept (b), use the equation of the line $y = mx + b$. Substitute one of the points and the calculated slope into the equation:

Using point (-4, 10):
\[ 10 = -\frac{5}{4}(-4) + b \]
\[ 10 = 5 + b \]
\[ b = 5 \]

The y-intercept is 5.

#### d. Writing the Linear Function
Combine the slope and y-intercept to write the equation of the line:

\[ y = -\frac{5}{4}x + 5 \]

This is the equation of the linear function passing through the points (-4, 10) and (8, -5).

### Diagram Explanation
The provided grid is an empty coordinate plane with both the x-axis and y-axis ranging from -10 to 10. The tool allows plotting and drawing lines to visualize the points and the resulting linear function.

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