solve for a. and b. **Understanding Linear Functions through Graph Analysis****Problem Statement:**The graph of a linear function $ f $ is shown to the right. **Tasks:**(a) Identify the slope, y-intercept, and x-intercept.(b) Write the equation that defines $ f $.**Graph Description:**The visual representation provided is a graph of a linear equation on a standard Cartesian plane with labeled axes. The graph includes both positive and negative values extending from -5 to 5 on the x-axis and y-axis. The linear function appears as a straight line sloping downwards from left to right, intersecting the y-axis at $ y = 4 $ and the x-axis at approximately $ x = 4 $.**Questions:****a) The slope is** ____ .(Type an integer or a simplified fraction.)**Instructions:**1. To find the slope ($ m $), use the formula $ m = \frac{\Delta y}{\Delta x} $, where $ \Delta y $ represents the change in the y-coordinates and $ \Delta x $ represents the change in the x-coordinates between two points on the line.2. Identify the exact y-intercept (where the line crosses the y-axis).3. Identify the exact x-intercept (where the line crosses the x-axis).By plugging the values from the graph into these steps, you should arrive at the slope and the full linear equation.**Solution Steps:**Starting with the visual details provided, let's solve:- y-intercept: $ y = 4 $- x-intercept: Near $ x = 4 $- Choose two points to find the rise over run (slope): - Point 1: (0,4) - Point 2: (4,0)Thus, slope $ m $ is:\[ m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1 \]Finally, substitute the identified intercept and slope into the slope-intercept form $ y = mx + b $:\[ y = -x + 4 \]This provides a full understanding of the relationship described by the graph.

Answered: Image /qna-images/answer/1d37c952-1a74-4542-b0b3-407bd1aca4b5.jpg

The graph of a linear function f is shown to the right. (a) Identify the slope, y-intercept, and x-intercept. (b) Write the equation that defines f. a) The slope is. (Type an integer or a simplified fraction.)

The graph of a linear function f is shown to the right. (a) Identify the slope, y-intercept, and x-intercept. (b) Write the equation that defines f. a) The slope is. (Type an integer or a simplified fraction.)

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

solve for a. and b.

**Understanding Linear Functions through Graph Analysis**

**Problem Statement:**
The graph of a linear function $ f $ is shown to the right.

**Tasks:**
(a) Identify the slope, y-intercept, and x-intercept.
(b) Write the equation that defines $ f $.

**Graph Description:**
The visual representation provided is a graph of a linear equation on a standard Cartesian plane with labeled axes. The graph includes both positive and negative values extending from -5 to 5 on the x-axis and y-axis. The linear function appears as a straight line sloping downwards from left to right, intersecting the y-axis at $ y = 4 $ and the x-axis at approximately $ x = 4 $.

**Questions:**

**a) The slope is** ____ .
(Type an integer or a simplified fraction.)

**Instructions:**
1. To find the slope ($ m $), use the formula $ m = \frac{\Delta y}{\Delta x} $, where $ \Delta y $ represents the change in the y-coordinates and $ \Delta x $ represents the change in the x-coordinates between two points on the line.
2. Identify the exact y-intercept (where the line crosses the y-axis).
3. Identify the exact x-intercept (where the line crosses the x-axis).

By plugging the values from the graph into these steps, you should arrive at the slope and the full linear equation.

**Solution Steps:**
Starting with the visual details provided, let's solve:

- y-intercept: $ y = 4 $
- x-intercept: Near $ x = 4 $
- Choose two points to find the rise over run (slope):
- Point 1: (0,4)
- Point 2: (4,0)

Thus, slope $ m $ is:
\[ m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1 \]

Finally, substitute the identified intercept and slope into the slope-intercept form $ y = mx + b $:
\[ y = -x + 4 \]

This provides a full understanding of the relationship described by the graph.

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