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,...

See similar textbooks

Related questions

Q: Given A = bh solve for b

Q: x+ y+ z = -4 2x+ 4y+ 2z -x+ 8y- 3z - 16 %3D -32 %3D

Q: Find the solution for an = 6a-1-8an-2 for n>2 and ao = 4, aj = 10.

A: Given recurrence relation is an=6an-1-8an-2, n≥2 and a0=4, a1=10. Let an=xn be a solution of above…

Q: 2. Solve for B. 30m 18m 22m

A: It is given that, We have to find B.

Q: Solve K= PRT for P. P=

Q: Solve. 3 x x 4 = -13

Q: Solve for w. 38= -6w - 7w - 27

Q: 1 2 C+ 3 4 5 6 1 D= 7 8 8 5

A: The above question is based on the concept of Matrices. We have to assume C and D as the two…

Q: Solve. 8 + √2x + 3 = 15

A: The given equation is; 8 + sqrt(2x+3) = 15

Q: 4-y² 2-y SŠ *-* zdxdzdy

A: Given: Let I=∫02∫04-y2∫02-y z dx dz dy To Find: To evaluate the given triple integration.

Q: Solve the following equation for c. 104c-5=d

Q: . Solve. Give each solution rounded to three decimal places. Show all steps! 312 300 + 300e-0.08z…

A: Given equation is : 312=300+300e-0.08x To find the value of x.

Q: Solve for a. c = ab

A: Given: c=ab

Q: 6. Solve the equation for x. V3x+2-3/2x-2 C. 8 a. 15 15 d. 8 b. x- 3

Q: b n Solve for p: y

Q: Solve for x and y. K 4y + 21 r+ 87 бу+9 P 2x + 103 X = II

A: Use property as shown below.

Q: Solve. B P+u for u ju

A: Given : Bj = P+uu

Q: a̟ = 48 and a = 24 Find a,

Q: Solve for b. Use all lower case letters. -(a + b) b = S =

Q: Solve the following equation: x= Jx +30 O A. 36 O B. 37 O C. 35 O D. Both A and B O E. Both B and C

Q: Solve for re(0, T csc² z = 4 CSC %3D

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

A =-bh 9. Solve for b. 2h 2A 2h 2A OType there to search
Solve for x and y if:2x + 3y = 5 and3x + 4y = 4
(3.35 x 109)(7.47 x 10*) =| 6.80 x 10 3.89 х 10 4 — 7.47 х 105 (2.38 x 10) (7.48 x 10) 9.35 x 106 ) (7.35 × 106 2.42 х 10
Solve. v-10 6. - v2 – 5v+4 v-1 v-4
Solve =R for K. K K =
7. Solve for A: (I – 3A")-1 = -2
Solve for X In(2xy. In) 2x+1 2メーS
33.) Solve 5y + 1.8 = 4y - 3.2 a. -5/9 b. 5/9 c. 5 d. -5