Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 38

Chapter 3, Problem 38

Use a graphing calculator to graph each equation in the standard viewing window. -2x + 5y = 10

Verified step by step guidance

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.

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Key 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.

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.

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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Find the slope and y-intercept of each line, and graph it. 4x-y =7

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Textbook Question

If a walkway rises 2.5 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? <Image>

A. 0.25, B. 4, C. 2.5/10, D. 25%, E. 1/4, F. 10/2.5, G. 400%, H. 2.5%

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