Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

In the figure above, lines \(p\) and \(q\) are graphed on the \(x y\)-plane. What is the \(x\)-intercept of line \(q\) ? A) 24 B) \(27.6\) C) \(33.8\) D) \(38.4\)

Short Answer

Expert verified
Without the provided figure, we are unable to find the exact equation of line q and determine the accurate x-intercept of line q in this case.

Step by step solution

01

Find the equation of line q

To find the equation of line q, we need to analyze the given figure. Unfortunately, the figure is not provided for this question. Thus, we can't find the exact equation of line q. Therefore, we can't proceed to the next step. However, if the equation of line q was provided or could be deduced from the provided figure, we could follow the steps below to find the x-intercept.
02

Set y to 0 in the equation of line q

Since we are looking for the x-intercept, we need to find where line q intersects the x-axis, which will have a y-coordinate of 0. Substitute 0 for y in the equation and solve for x. For example, if the equation of line q was \(y = mx + b\) (with specific values for m and b), we would set y to 0 and solve for x: \(0 = mx + b\)
03

Solve for x

Now, rearrange the equation to solve for x. Continuing with the hypothetical equation: \(-mx = b\) \(x = -\frac{b}{m}\) This would give us the x-intercept of the line q.
04

Choose the correct answer

Once the x-intercept is found by following the steps above, compare the result with the given options (A, B, C, and D). Select the option that matches the calculated x-intercept. Remember that this solution assumes having enough information to find the equation of line q. As the figure is not provided in the question, we cannot determine the accurate x-intercept of line q in this case.

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.

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

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Linear Equations
Linear equations are the simplest type of equations in algebra and they have widespread applications in mathematics, especially in coordinate geometry. A linear equation in two variables, x and y, can always be written in the form of y = mx + b, where m represents the slope of the line and b is the y-intercept, the point where the line crosses the y-axis.

To identify the x-intercept from a linear equation, we seek the value of x when y is zero. In a simple equation like y = mx + b, setting y to zero and solving for x yields the x-intercept.

For instance, if we have y = 2x + 3, finding the x-intercept involves setting y to zero:
\[0 = 2x + 3\] Solving this gives us: \[x = -\frac{3}{2}\] This value of x is where the line crosses the x-axis. The concept of finding an x-intercept is central to understanding how linear equations graphically represent solutions.
Coordinate Geometry
Coordinate geometry, also known as analytic geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry where no use of numbers to represent geometric figures is made. It allows us to precisely discuss the relationship between algebraic equations and geometric figures. The x-intercept we discussed earlier is a key example of coordinate geometry in action.

The x-axis and y-axis divide the plane into four quadrants, which provides a system for describing exact locations, called coordinates, of points on the plane. In the case of finding an x-intercept on the coordinate plane, we are interested in the point's horizontal position relative to the origin.

An important technique in coordinate geometry is plotting lines and curves by taking various values of x and y that satisfy an equation. By connecting these points, the geometric figure represented by the equation is revealed. Points where lines or curves intersect the axes are of particular importance: the x-intercept and y-intercept are the points where the figure intersects the x-axis and y-axis respectively.
SAT Math
For students preparing for the SAT, the knowledge of how to find the x-intercept of a line is essential as it is a frequent topic in the math section. Students must understand linear equations and coordinate geometry to tackle these questions effectively. Problems involving x-intercepts in the SAT math section may require you to analyze graphs, interpret equations, or apply properties of algebraic functions.

Beyond the ability to solve for x-intercepts algebraically, visual understanding through graphs can also be tested. SAT math questions may provide a graphed line and ask for the x-intercept, which requires the student to read and analyze the graph correctly. It is also possible that the SAT may ask students to understand the relationship between different forms of linear equations, like slope-intercept form and standard form, and how those affect finding an x-intercept.

In the context of SAT preparation, practicing with problems of varying difficulty and understanding their step-by-step solutions helps in developing a stronger grasp of the topic. It's important to not just memorize processes, but also understand the reasoning behind them to cultivate a deeper comprehension and flexibility in problem-solving during the exam.

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

Robert is selling televisions at an electronics store. The televisions normally cost \(\$ 545\) each but are being sold at an \(8 \%\) discount. What is the minimum number of televisions Robert must sell if he wants to meet his quota of \(\$ 100,000\) in total sales?

The writer wants to introduce one of the main ideas of the passage. Which choice best accomplishes this goal? A) NO CHANGE B) despite the fact that the organization would have earned money from the performance. C) even though Anderson had just completed a very successful European tour. D) which is something that unfortunately had happened to Anderson before.

A poll of 400 randomly selected likely voters in Seanoa City was taken to determine the support for the mayoral candidates in the upcoming election. Of the likely voters selected, 190 stated that they are likely to vote for Candidate \(\mathrm{A}\). If the conclusion is drawn that "approximately 3,120 voters are likely to vote for Candidate A," which of the following is closest to the number of likely voters in Seanoa City? A) 1,482 B) 3,120 C) 4,741 D) 6,568 $$ \begin{gathered} y^2=21-x \\ x=5 \end{gathered} $$

The amount of carbon- 15 in a given sample decays exponentially with time. If the function \(C(m)=100\left(\frac{1}{2}\right)^{24 m}\) models the amount of carbon-15 remaining in the sample after \(m\) minutes, which of the following must be true? A) The amount of carbon in the sample halves every minute. B) The amount of carbon in the sample halves every 24 minutes. C) The amount of carbon in the sample halves 24 times every minute. D) The amount of carbon in the sample reduces by a factor of 24 every 2 minutes.

An investor is deciding between two options for a short-term investment. One option has a return \(R\), in dollars, \(t\) months after investment, and is modelled by the equation \(R=100\left(3^t\right)\). The other option has a return \(R\), in dollars, \(t\) months after investment, and is modeled by the equation \(R=350 t\). After 4 months, how much less is the return given by the linear model than the return given by the exponential model? A) \(\$ 1,400\) B) \(\$ 4,050\) C) \(\$ 6,700\) D) \(\$ 8,100\) $$ n-\sqrt{2 n+22}=1 $$

See all solutions

Recommended explanations on English Textbooks

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