Problem 175 Find the intercepts for each equ... [FREE SOLUTION]

Chapter 4: Problem 175

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

Short Answer

Expert verified

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

Step by step solution

- Find the y-intercept

To find the y-intercept, set x = 0 in the equation and solve for y. For the equation y = 3x, we have y = 3(0) = 0. Therefore, the y-intercept is (0,0).

- Find the x-intercept

To find the x-intercept, set y = 0 in the equation and solve for x. For the equation y = 3x, we get 0 = 3x. Dividing both sides by 3, we get x = 0. Therefore, the x-intercept is (0,0).

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Key Concepts

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

y-intercept

The y-intercept of a linear equation is where the line crosses the y-axis. To find it, we set the variable x to zero and solve for y. The logic is simple: at the y-axis, any point will have an x-coordinate of 0. For instance, the y-intercept of the equation \( y = 3x \) is found by setting \( x = 0 \). This results in \( y = 3(0) = 0 \). Thus, the y-intercept is the point (0, 0). Considering the ordered pair (x, y), this means when x is 0, y equals 0.

x-intercept

The x-intercept of a linear equation is where the line crosses the x-axis. To find it, we set the variable y to zero and solve for x. This is because at the x-axis, any point will have a y-coordinate of 0. Taking our example, the x-intercept of the equation \( y = 3x \) can be determined by setting \( y = 0 \). This gives \( 0 = 3x \). Solving this, we divide both sides by 3 to obtain \( x = 0 \). Hence, the x-intercept is the point (0, 0).

linear equations

Linear equations are mathematical expressions that represent straight lines when plotted on a graph. They are typically written in the form \( y = mx + b \), where \( m \) is the slope (indicating how steep the line is), and \( b \) is the y-intercept (where the line crosses the y-axis). Linear equations have constant rates of change, meaning the slope is the same regardless of where you measure on the line.

When working with linear equations, it鈥檚 important to know how to identify key features such as the slope and intercepts, as these provide valuable information about the line鈥檚 behavior on a graph:

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91影视

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

Short Answer

Step by step solution

- Find the y-intercept

- Find the x-intercept

Key Concepts

y-intercept

x-intercept

linear equations

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