Textbook Question
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
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3. Functions
Intro to Functions & Their Graphs
2:15 minutesProblem 37
Textbook Question
Use a graphing calculator to graph each equation in the standard viewing window. 3x + 4y = 6
Verified step by step guidance1
Rewrite the given equation \(3x + 4y = 6\) in slope-intercept form \(y = mx + b\) by isolating \(y\). Start by subtracting \(3x\) from both sides: \(4y = -3x + 6\).
Next, divide every term by 4 to solve for \(y\): \(y = \frac{-3}{4}x + \frac{6}{4}\). Simplify the fraction \(\frac{6}{4}\) if possible.
Turn on your graphing calculator and enter the function \(y = -\frac{3}{4}x + \frac{3}{2}\) into the function input (usually labeled as \(Y=\)).
Set the graphing window to the standard viewing window, which typically has \(x\) and \(y\) values ranging from -10 to 10. This ensures you see the main features of the graph.
Graph the equation and observe the line. Note the slope \(-\frac{3}{4}\) which indicates the line falls 3 units vertically for every 4 units it moves horizontally, and the y-intercept \(\frac{3}{2}\) where the line crosses the y-axis.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Form of a Linear Equation
The standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants. Understanding this form helps in identifying the coefficients and constants needed to graph the line or convert it into slope-intercept form for easier plotting.
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Standard Form of Line Equations
Graphing Linear Equations Using a Calculator
Graphing calculators allow you to input equations and visualize their graphs quickly. For linear equations, you often need to solve for y or use the calculator’s function input to plot the line within the standard viewing window, typically set from -10 to 10 on both axes.
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Standard Viewing Window
The standard viewing window on a graphing calculator usually ranges from -10 to 10 on both the x- and y-axes. Knowing this helps you anticipate how the graph will appear and ensures the important features of the line, such as intercepts, are visible within this range.
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