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Chapter 11: Problem 133

In the following exercises, find the intercepts. $$ x-y=-3 $$

Short Answer

Expert verified
The x-intercept is (-3, 0) and the y-intercept is (0, 3).

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. Using the equation:\[ x - y = -3 \]Set y = 0:\[ x - 0 = -3 \]So, the x-intercept is\[ x = -3 \]The x-intercept is (-3, 0).
02

Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. Using the equation:\[ x - y = -3 \]Set x = 0:\[ 0 - y = -3 \]So, the y-intercept is\[ y = 3 \]The y-intercept is (0, 3).

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Key Concepts

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

x-intercept and how to find it
The x-intercept of a linear equation is the point where the line crosses the x-axis. At this point, the value of y is zero. To find the x-intercept, you need to set y to 0 in the equation and solve for x.
In the equation given: \[ x - y = -3 \], you follow these steps:
  • Set y to 0: \[ x - 0 = -3 \],
  • Then solve for x: x = -3.
This means the x-intercept occurs at the point (-3, 0). It's that simple! Whenever you have a linear equation, just plug y as 0, solve for x, and you will get your x-intercept.
This point tells you where the graph touches the x-axis.
y-intercept and how to find it
The y-intercept is the point where the line crosses the y-axis. At this point, the value of x is zero. To find the y-intercept, you need to set x to 0 in the equation and solve for y.
Let's use the same equation: \[ x - y = -3 \], and follow these steps:
  • Set x to 0: \[ 0 - y = -3 \],
  • Then solve for y: y = 3.
So, the y-intercept occurs at the point (0, 3).
This method can be applied to any linear equation. Just plug x as 0, solve for y, and you will get your y-intercept. This point shows where the graph touches the y-axis.
Solving equations for intercepts
Solving equations to find intercepts is a fundamental skill in algebra. Intercepts help us understand the behavior of linear equations. Here's a quick summary of the steps needed:
  • To find the x-intercept: Set y = 0 and solve for x.
  • To find the y-intercept: Set x = 0 and solve for y.
In both steps, you essentially isolate the variable you need.
For x-intercept: \[ x - y = -3 \], set y to 0, isolate x: \[ x = -3 \]
For y-intercept: \[ x - y = -3 \], set x to 0, isolate y: \[ y = 3 \]
With these steps, you'll always be able to find the intercepts of any linear equation. This makes graphing and understanding relationships between variables much easier.

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