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Chapter 11: Problem 170

In the following exercises, graph using the intercepts. $$ 2 x-y=-8 $$

Short Answer

Expert verified
Plot (-4, 0) and (0, 8), then 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. The equation is: \[ 2x - y = -8 \]When y = 0:\[ 2x - 0 = -8 \] This simplifies to:\[ 2x = -8 \]Divide both sides by 2:\[ x = -4 \]So, the x-intercept is (-4, 0).
02

Find the y-intercept

To find the y-intercept, set x to 0 in the equation. The equation is: \[ 2x - y = -8 \]When x = 0:\[ 2(0) - y = -8 \]This simplifies to:\[ -y = -8 \]Divide both sides by -1:\[ y = 8 \]So, the y-intercept is (0, 8).
03

Plot the intercepts

Plot the points (-4, 0) and (0, 8) on the coordinate plane. These are the intercepts found in the previous steps.
04

Draw the line

Draw a straight line through the points (-4, 0) and (0, 8). This is the graph of the equation \(2x - y = -8\).

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Key Concepts

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

x-intercept
The x-intercept of an equation is the point where the graph crosses the x-axis. This happens when the y value is zero. To find the x-intercept for the equation \(2x - y = -8\), you set y to 0 and solve for x. After placing y = 0 in the equation, it becomes \(2x = -8\). Dividing both sides by 2, you get x = -4. Therefore, the x-intercept is ( -4, 0). This means the graph crosses the x-axis at the point (-4, 0).
y-intercept
The y-intercept is the point where the graph crosses the y-axis. This is when the x value is zero. To find the y-intercept of the equation \(2x - y = -8\), you set x to 0 and solve for y. By making x = 0 in the equation, it turns into \(-y = -8\). Dividing by -1, you will get y = 8. Therefore, the y-intercept is (0, 8), indicating that the graph crosses the y-axis at the point (0, 8).
coordinate plane
A coordinate plane is a two-dimensional surface where we can plot points, lines, and curves. It consists of a horizontal axis (x-axis) and a vertical axis (y-axis). The point where these axes intersect is called the origin, labeled as (0, 0).
On a coordinate plane, each point is represented by an ordered pair (x, y), where x shows the position along the x-axis and y shows the position along the y-axis. When graphing linear equations, we use the coordinate plane to visually represent the solutions. For example, the points (-4, 0) and (0, 8) from the equation 2x - y = -8 can be plotted on the coordinate plane to help draw the line.
linear equations
Linear equations are equations of the first degree, which means they graph as straight lines on a coordinate plane. They have the general form Ax + By = C, where A, B, and C are constants.
Linear equations are simple to work with and interpret. The solutions to these equations are sets of x and y values that satisfy the equation. To graph a linear equation, we often find the x-intercept and y-intercept first. By plotting these intercepts, we create a line that represents all the solutions to the equation. For instance, with 2x - y = -8, finding the intercepts (-4, 0) and (0, 8) and drawing a line through them shows the graph of the equation.

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