Question

Graph each linear equation. $x-y=5$

   Graph each linear equation.
$x-y=5$

Beginning Algebra

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 3, Problem 34

Instant Answer

Solved by Expert Brandon Fox

06/19/2020

Step 1

To do this, we set x to 0 in the equation $x - y = 5$. This gives us $0 - y = 5$, which simplifies to $-y = 5$. Dividing both sides by -1, we get $y = -5$. So, the y-intercept of the equation is -5. Show more…

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Graph each linear equation. $x-y=5$

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Key Concepts

Slope

The slope in a linear equation measures the rate of change of y with respect to x, indicating both the steepness and the direction (positive, negative, zero, or undefined) of the line. It is calculated as the ratio of the vertical change to the horizontal change between any two distinct points on the line.

Graphing Techniques

Graphing a linear equation involves locating the y-intercept on the graph, then using the slope to determine additional points on the line. Once two or more points are plotted, they can be connected with a straight line that extends in both directions.

Linear Equation

A linear equation represents a straight line in a coordinate plane and is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. This form helps in quickly identifying the nature of the line and plotting it on a graph.

Slope-Intercept Form

The slope-intercept form (y = mx + b) is a standard way of writing linear equations that makes it straightforward to graph the line by identifying the slope, which determines the steepness, and the y-intercept, which is where the line crosses the y-axis.

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