Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 18

The graph of a line in the \(x y\)-plane passes through the point \((-2, k)\) and crosses the \(x\)-axis at the point \((-4,0)\). The line crosses the \(y\)-axis at the point \((0,12)\). What is the value of \(k\) ? $$ 5\left(10 x^2-300\right)+\left(9,844+50 x^2\right) $$

Short Answer

Expert verified
The value of \(k\) is 6 for the given line passing through the point \((-2, k)\), crossing the x-axis at \((-4,0)\) and the y-axis at \((0,12)\).

Step by step solution

01

Find the slope of the line

We are given two points on the line: \((-4,0)\) and \((0,12)\). To find the slope of this line, we can use the formula: $$m = \frac{y2 - y1}{x2 - x1}$$ Now, insert the values of the given points (-4,0) and (0,12) into the equation: $$m = \frac{12 - 0}{0 - (-4)}$$
02

Calculate the slope

Use the equation with the given values to find the slope m: $$m = \frac{12}{4}$$ $$m = 3$$ So, the slope of the line is m = 3.
03

Find the equation of the line

Now, we will use the point-slope form of a linear equation: $$y - y1 = m(x - x1)$$ Since the line crosses the y-axis at (0,12), we can use the point (0,12) and the slope found in Step 2: $$y - 12 = 3(x - 0)$$
04

Simplify the equation for the line

Simplify the equation found in Step 3 to get the line's equation in slope-intercept form (y = mx + b): $$y - 12 = 3x$$ $$y = 3x + 12$$ Now we have the equation of the line as \(y = 3x +12\).
05

Find the value of k

We are given the point \((-2, k)\), so we can find the value of \(k\) by substituting the x-coordinate into the line's equation: $$k = 3(-2) + 12$$ $$k = -6 + 12$$ $$k = 6$$ So, the value of \(k\) is 6, and the point is \((-2, 6)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Both authors would most likely agree that any social changes undertaken to fight poverty would be A) likely to completely solve the problems of financial inequality. B) a stopgap measure needed to prevent the wealthy from keeping their money. C) unsuccessful without a drastic change in the mindset of the poor. D) partial solutions that would present new sets of challenges.

The number of bacteria colonies \(h\) hours after the beginning of an experiment is given by the function \(C(h)=3^h-2 h+20\). What does the number 20 represent in the function? A) The final rate of growth, in colonies per hour B) The initial rate of growth, in colonies per hour C) One less than the initial number of bacteria colonies D) One more than the final number of bacteria colonies $$ \begin{aligned} &\text { Agricultural Land as a Percent of Total Land Area, } 2014\\\ &\begin{array}{|l|c|} \hline \multicolumn{1}{|c|}{\text { Country }} & \text { Percent of Total Land Area } \\ \hline \text { Brazil } & 33.8 \% \\ \hline \text { Canada } & 7.2 \% \\ \hline \text { Greenland } & 0.6 \% \\ \hline \text { Latvia } & 30.1 \% \\ \hline \text { Mexico } & 54.9 \% \\ \hline \text { New Zealand } & 42.2 \% \\ \hline \text { Russian Federation } & 13.3 \% \\ \hline \text { Turkey } & 50.1 \% \\ \hline \text { United States } & 44.6 \% \\ \hline \end{array} \end{aligned} $$

Andrew works out for 30 minutes every other day. If he spends \(35 \%\) of his workout time one day waiting for the weight rack, how many seconds of that day's workout did he spend waiting for the weight rack? A) 630 B) 35 C) 21 D) \(10.5\)

A psychology student randomly selected 300 people from a group of people who indicated that they preferred to work alone. Those 300 people were given a task to work on individually and then asked whether they were happy or unhappy while doing the task. Of those surveyed, \(5 \%\) stated they were unhappy while doing the task. Which of the following inferences can appropriately be drawn from this survey result? A) Few people who prefer working alone will be unhappy doing this task. B) Few people who do not prefer working alone will be happy doing this task. C) Less than \(5 \%\) of people will be happy doing this task if they do not work alone. D) Less than \(5 \%\) of people will be unhappy doing this task if they work alone.

What does the author suggest about tourism? A) It was most vibrant in the mid-20th century. B) Eco-tourism will be an important part of the future economy in the region. C) Tourism may provide more benefit to the Dead Sea region’s economy than agriculture currently does. D) Officials in the tourism and agriculture industries should work together to create policy.
See all solutions

Recommended explanations on English Textbooks

Essay Writing Skills

Read Explanation

Language and Social Groups

Read Explanation

Morphology

Read Explanation

Global English

Read Explanation

Essay Prompts

Read Explanation

Argumentative Essay

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free