Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The graph in the xy-plane of the linear function f contains the point (3 , 4). For every increase of 5 units in x, f(x) increases by 3 units. Which of the following equations defines the function?

$f (x) = - \frac{5}{3} x + 9$
$f (x) = - \frac{3}{5} x + \frac{29}{5}$
$f (x) = \frac{3}{5} x + \frac{11}{5}$
$f (x) = \frac{5}{3} x - 1$

The correct answer is: $straight f left parenthesis straight x right parenthesis space equals space 3 over 5 straight x space plus space 11 over 5$

HINT:- find slope of the line by using the given condition . Now, form a slope intercept form of the equation to substitute the given (3 , 4) co-ordinates in the equation to get the intercept and finding the equation.
Given, the increase in x by 5 units (dx = +5) gives the f(x) to be increased by 3 units (d(f(x)) = dy = +3)
Step 1:- finding slope of the line
slope is given by $dy over dx$ = $3 over 5$
Slope of equation m = $3 over 5$
Step 2:- form the slope intercept form
y = mx + c ,substitute m = $3 over 5$ .
We get y = $3 over 5$ x + c
Step 3 : find c by substituting (3 , 4) in y = $3 over 5$ x + c.
$4 space equals fraction numerator begin display style 3 end style over denominator 5 end fraction space cross times space left parenthesis 3 right parenthesis space plus space c space not stretchy rightwards double arrow space c space equals space 4 space minus space open parentheses fraction numerator begin display style 9 end style over denominator 5 end fraction close parentheses$
$not stretchy rightwards double arrow space straight c space equals space fraction numerator begin display style 11 end style over denominator 5 end fraction$
The final equation of linear function is $straight f left parenthesis straight x right parenthesis space equals space straight y space equals space 3 over 5 straight x space plus space 11 over 5$ .

Related Questions to study

f (x) = x³ + 3x² - 6x -1
For the function f defined above, what is the value of f (-1)?

f (x) = x³ + 3x² - 6x -1
For the function f defined above, what is the value of f (-1)?

2x³ + 11x² + 5x
Which of the following is NOT a factor of the polynomial above?

2x³ + 11x² + 5x
Which of the following is NOT a factor of the polynomial above?

The expression $fraction numerator x to the power of negative 2 end exponent y to the power of 1 half end exponent over denominator x to the power of 1 third end exponent y to the power of negative 1 end exponent end fraction$ , where x > 1 and y > 1, is equivalent to which of the following?

The expression $fraction numerator x to the power of negative 2 end exponent y to the power of 1 half end exponent over denominator x to the power of 1 third end exponent y to the power of negative 1 end exponent end fraction$ , where x > 1 and y > 1, is equivalent to which of the following?

parallel

ax³ + bx² + cx + d = 0
In the equation above, a, b, c, and d are constants. If the equation has roots −1, −3, and 5, which of the following is a factor of ax³ + bx² + cx + d = 0

ax³ + bx² + cx + d = 0
In the equation above, a, b, c, and d are constants. If the equation has roots −1, −3, and 5, which of the following is a factor of ax³ + bx² + cx + d = 0

2x² - 2 = 2x + 3
Which of the following is a solution to the equation above?

2x² - 2 = 2x + 3
Which of the following is a solution to the equation above?

What is the solution to-
- 3 (x - 5) = - 2x + 4?

What is the solution to-
- 3 (x - 5) = - 2x + 4?

parallel

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

$fraction numerator 2 space left parenthesis straight x space plus space 1 right parenthesis over denominator straight x space plus space 5 end fraction space equals space 1 space minus space fraction numerator 1 over denominator straight x space plus space 5 end fraction$
What is the solution to the equation above?

$fraction numerator 2 space left parenthesis straight x space plus space 1 right parenthesis over denominator straight x space plus space 5 end fraction space equals space 1 space minus space fraction numerator 1 over denominator straight x space plus space 5 end fraction$
What is the solution to the equation above?

Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

parallel

During a sale, the cost of each shirt is $ 15 and that of each pair of pants is $ 25. Geoff can spend at most $ 120 at the store. If Geoff buys s shirts and p pairs of pants, which of the following must be true?

During a sale, the cost of each shirt is $ 15 and that of each pair of pants is $ 25. Geoff can spend at most $ 120 at the store. If Geoff buys s shirts and p pairs of pants, which of the following must be true?

Blood volume, V_B, in a human can be determined using the equation $straight V subscript straight B space equals space fraction numerator straight V subscript straight P over denominator 1 space minus space straight H end fraction$
, where V_P is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume ?

Blood volume, V_B, in a human can be determined using the equation $straight V subscript straight B space equals space fraction numerator straight V subscript straight P over denominator 1 space minus space straight H end fraction$
, where V_P is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume ?

x² + 6x + 4 Which of the following is equivalent to the expression above?

x² + 6x + 4 Which of the following is equivalent to the expression above?

parallel

A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant rate for 12 years, after which it is considered to have no monetary value. How much is the camera equipment worth 4 years after it is purchased?

A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant rate for 12 years, after which it is considered to have no monetary value. How much is the camera equipment worth 4 years after it is purchased?

In the figure above, line t intersects lines $calligraphic l$ and k. Which of the following statements, if true, would imply that lines $calligraphic l$ and k are parallel?

In the figure above, line t intersects lines $calligraphic l$ and k. Which of the following statements, if true, would imply that lines $calligraphic l$ and k are parallel?

If f( x) = $fraction numerator x squared space minus space 6 x space plus space 3 over denominator x space minus space 1 end fraction$ , what is f(-1) ?

If f( x) = $fraction numerator x squared space minus space 6 x space plus space 3 over denominator x space minus space 1 end fraction$ , what is f(-1) ?

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.