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Chapter 4: Problem 189

Graph using the intercepts. \(x-y=-4\)

Short Answer

Expert verified
The intercepts are (-4, 0) and (0, 4). Plot these points and draw a line through them.

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y to 0 in the equation and solve for x. The equation is \[ x - y = -4 \]Substitute y = 0:\[ x - 0 = -4 \]Thus,\[ x = -4 \]So, the x-intercept is (-4, 0).
02

Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. The equation is \[ x - y = -4 \]Substitute x = 0:\[ 0 - y = -4 \]Thus,\[ y = 4 \]So, the y-intercept is (0, 4).
03

Plot the intercepts

Plot the points (-4, 0) and (0, 4) on a graph.
04

Draw the line

Draw a straight line through the points (-4, 0) and (0, 4). This line represents the graph of the equation \( x - y = -4 \).

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Key Concepts

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

x-intercept
To find the x-intercept of a linear equation, you need to set the y-variable to zero and solve for x. This is like asking where the line crosses the x-axis. For the equation given, which is \( x-y=-4 \), set y to 0 and solve for x. Our equation becomes \( x - 0 = -4 \). Clearly, \( x = -4 \). This means the x-intercept is at the point \( (-4, 0) \). The x-intercept is critical because it tells us one exact point where the line intersects the x-axis, allowing us to plot part of the graph accurately.
y-intercept
Finding the y-intercept of a linear equation is just as crucial as finding the x-intercept. Here, you'll set the x-variable to zero and solve for y. In our equation \( x-y=-4 \, setting x to 0 simplifies it to \ (0-y=-4) \). Solving for y gives us \( y=4 \). This means the y-intercept is at the point \( (0, 4) \). The y-intercept tells us exactly where the line cuts through the y-axis, offering another specific point we can use to map out the line accurately on the graph.
plotting points
Plotting points on a graph is a crucial step in graphing linear equations. After finding both the x-intercept and the y-intercept, we plot these points on the coordinate plane.
  • First, plot the x-intercept, (-4, 0). This point is 4 units to the left of the origin along the x-axis.
  • Next, plot the y-intercept, (0, 4). This point is 4 units above the origin along the y-axis.
With these points plotted, we have two specific locations that our line will pass through, helping us set up the graph accurately.
drawing a line
Once you have plotted the necessary points, in this case, the x-intercept and y-intercept, it's time to draw the line. Simply use a ruler or a straightedge to connect the points
  • The straight line through (鈭�4, 0) and (0, 4) represents our graph
Ensure the line extends through both points and continues beyond them. This represents all possible (x, y) pairs that solve the equation \( x - y = -4 \). Drawing the line through these intercepts ensures that every point on the line is a solution to the original linear equation.

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