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Chapter 4: Problem 166

Find the intercepts for each equation. . \(5 x-y=5\)

Short Answer

Expert verified
The intercepts are (1, 0) for x and (0, -5) for y.

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. Start with the equation: 5x - y = 5 Set y = 0: 5x - 0 = 5 Simplify: 5x = 5 Divide both sides by 5: x = 1. Thus, the x-intercept is at the point (1, 0).
02

Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. Start with the equation: 5x - y = 5 Set x = 0: 5(0) - y = 5 Simplify: -y = 5 Divide both sides by -1: y = -5. Thus, the y-intercept is at the point (0, -5).

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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 line is the point where the line crosses the x-axis. This means that at the x-intercept, the value of y is always zero. To find the x-intercept, we substitute y with 0 in the equation and solve for x. Here's a step-by-step process:

Start with the given equation:
5x - y = 5
Set y = 0:
5x - 0 = 5
This simplifies to:
5x = 5
Now, solve for x by dividing both sides of the equation by 5:
x = 1

Therefore, the x-intercept is at the point (1, 0). Remember, the x-intercept tells us where our graph will cross the x-axis, which is crucial for graphing linear equations.
y-intercept
The y-intercept of a line is the point where the line crosses the y-axis. At this point, the x value is always zero. To find the y-intercept, we set x to 0 and solve for y. Let's go through the steps:

Start with the given equation:
5x - y = 5
Set x = 0:
5(0) - y = 5
This simplifies to:
-y = 5
Now, solve for y by dividing both sides by -1:
y = -5

Thus, the y-intercept is at the point (0, -5). Knowing the y-intercept helps to understand where the line will cross the y-axis, which is an essential part of graphing linear relationships.
solving linear equations
Solving linear equations involves finding the value(s) of the variable(s) that make the equation true. Linear equations can be written in the form Ax + By = C. To solve for a specific variable, follow these general steps:

  • Isolate the variable you are solving for by getting all other terms on the opposite side of the equation.

  • Simplify the equation step-by-step, often by performing operations like addition, subtraction, multiplication, or division.

Let's apply this to our example equation, 5x - y = 5.
If finding x-intercept, set y to 0 and solve for x.
If finding y-intercept, set x to 0 and solve for y.

For both intercepts, the idea is to isolate one variable at a time and solve for it. This method not only solves for intercepts but also provides a fundamental approach to handling linear equations. Practice makes perfect, so try solving different linear equations to get more comfortable with these steps.

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Most popular questions from this chapter

Graph the linear inequality \(3 x+2 y \geq-6\)

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Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation \(S=400+0.15 c\) models the relation between her weekly salary, \(S\), in dollars and the amount of her sales, \(c\), in dollars. (a) Find Cherie's salary for a week when her sales were 0 (b) Find Cherie's salary for a week when her sales were 3600 . (c) Interpret the slope and S-intercept of the equation. (d) Graph the equation.

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