Textbook Question
Use a graphing calculator to graph each equation in the standard viewing window. 3x + 4y = 6
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3. Functions
Intro to Functions & Their Graphs
2:16 minutesProblem 38
Textbook Question
Use a graphing calculator to graph each equation in the standard viewing window. -2x + 5y = 10
Verified step by step guidance1
Rewrite the given equation \(-2x + 5y = 10\) in slope-intercept form \(y = mx + b\) by isolating \(y\). Start by adding \(2x\) to both sides: \(5y = 2x + 10\).
Next, divide every term by 5 to solve for \(y\): \(y = \frac{2}{5}x + 2\). This is the equation in slope-intercept form, where the slope \(m = \frac{2}{5}\) and the y-intercept \(b = 2\).
Turn on your graphing calculator and enter the equation \(y = \frac{2}{5}x + 2\) into the function input (usually labeled as \(Y=\)).
Use the standard viewing window on your calculator, which typically has \(x\) values from \(-10\) to \(10\) and \(y\) values from \(-10\) to \(10\), to graph the line.
Observe the graph to confirm that the line crosses the y-axis at \(2\) and rises with a slope of \(\frac{2}{5}\), meaning it goes up 2 units for every 5 units it moves to the right.
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 Ax + By = C, where A, B, and C are constants. Understanding this form helps in identifying the coefficients of x and y, which are essential for graphing the line and converting to other forms like slope-intercept.
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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 in terms of x or use the calculator's function input to plot the line within the standard viewing window.
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Standard Viewing Window
The standard viewing window on a graphing calculator typically ranges from -10 to 10 on both axes. Knowing this helps ensure the graph is displayed properly and that key points like intercepts are visible for analysis.
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