Problem 57 Find the $x$ - and $y$ -inte... [FREE SOLUTION]

Chapter 3: Problem 57

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line. $$y=-\frac{1}{2} x-20$$

Short Answer

Expert verified

The y-intercept is (0, -20) and the x-intercept is (-40, 0). Plot these points and draw the line.

Step by step solution

Find the y-intercept

The y-intercept is found by setting x = 0 in the equation. Substitute x = 0 into the equation: \[ y = -\frac{1}{2} \times 0 - 20 = -20 \] Therefore, the y-intercept is (0, -20).

Find the x-intercept

The x-intercept is found by setting y = 0 in the equation. Substitute y = 0 into the equation and solve for x: \[ 0 = -\frac{1}{2} x - 20 \] Rearrange and solve for x: \[ \frac{1}{2} x = -20 \] \[ x = -20 \times 2 = -40 \] Therefore, the x-intercept is (-40, 0).

Graph the line

To graph the line, plot the intercepts found in the previous steps: (0, -20) and (-40, 0). Draw a line through these points to represent the equation $ y = -\frac{1}{2} x - 20 $.

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Key Concepts

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

x-intercept

In a linear equation, the x-intercept is where the line crosses the x-axis. This happens when y equals zero. To find the x-intercept, substitute y = 0 into the equation and solve for x.

For the given equation: \[ y = -\frac{1}{2} x - 20 \] Set y = 0: \[ 0 = -\frac{1}{2} x - 20 \] This means: \[ \frac{1}{2} x = -20 \] To isolate x, multiply both sides by 2: \[ x = -40 \] So, the x-intercept is at the point (-40, 0).

When you graph it, you will place a point on the x-axis at -40. This is where the line will cross horizontally.

y-intercept

The y-intercept of a line is where the line crosses the y-axis. This happens when x equals zero. To find the y-intercept, substitute x = 0 into the equation and solve for y.

For the given equation: \[ y = -\frac{1}{2} x - 20 \] Set x = 0: \[ y = -\frac{1}{2} \times 0 - 20 = -20 \] So, the y-intercept is at the point (0, -20).

When you graph it, you will place a point on the y-axis at -20. This is where the line will cross vertically.

slope-intercept form

The slope-intercept form of a linear equation is written as: \[ y = mx + b \] Where:

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91影视

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$y=-\frac{1}{2} x-20$$

Short Answer

Step by step solution

Find the y-intercept

Find the x-intercept

Graph the line

Key Concepts

x-intercept

y-intercept

slope-intercept form

One App. One Place for Learning.

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