Problem 152 Find the intercepts for each equ... [FREE SOLUTION]

Chapter 4: Problem 152

Find the intercepts for each equation. \(x+y=3\)

Short Answer

Expert verified

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

Step by step solution

Find the x-intercept

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

Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. Set x = 0: \(0 + y = 3\) \(y = 3\)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

The x-intercept of a linear equation is the point where the graph crosses the x-axis. At this point, the value of y is always zero.
To find the x-intercept, follow these steps:

Set y to 0 in the equation.
Solve for x.

Let's use the given equation:
1. Set y to 0:
x + 0 = 3
2. Solve for x:
x = 3
So, the x-intercept is (3, 0).
This means that when y equals 0, x equals 3 and the graph crosses the x-axis at (3, 0).

y-intercept

The y-intercept of a linear equation is the point where the graph crosses the y-axis. At this point, the value of x is always zero.
To find the y-intercept, follow these steps:

Set x to 0 in the equation.
Solve for y.

Let's use the given equation:
1. Set x to 0:
0 + y = 3
2. Solve for y:
y = 3
So, the y-intercept is (0, 3).
This means that when x equals 0, y equals 3 and the graph crosses the y-axis at (0, 3).

linear equations

Linear equations are equations that produce a straight line when graphed.
They are usually written in the form:
ax + by = c, where a, b, and c are constants.
An important feature of linear equations is that the relationship between x and y is consistent; it doesn鈥檛 change.
These equations can have one x-intercept and one y-intercept.
To interpret a linear equation:

Identify its intercepts.
Plot those points on a graph.
Draw a straight line through both points.

For the given equation: x + y = 3
Setting y to 0 gives you the x-intercept, and setting x to 0 gives you the y-intercept. Use these intercepts to draw the line on a graph.
Understanding these core concepts will help you tackle any linear equation and find its intercepts.

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91影视

Find the intercepts for each equation. \(x+y=3\)

Short Answer

Step by step solution

Find the x-intercept

Find the y-intercept

Key Concepts

x-intercept

y-intercept

linear equations

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