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Chapter 3: Problem 69

Find all intercepts for each line. Some of these lines have only one intercept. $$3 x-5 y=15$$

Short Answer

Expert verified
The intercepts are (5, 0) and (0, -3).

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y = 0 in the equation and solve for x.Starting with the equation:\[3x - 5y = 15\]Set y = 0:\[3x - 5(0) = 15\]\[3x = 15\]Solve for x:\[x = 5\]So, the x-intercept is (5, 0).
02

Find the y-intercept

To find the y-intercept, set x = 0 in the equation and solve for y.Starting with the equation:\[3x - 5y = 15\]Set x = 0:\[3(0) - 5y = 15\]\[-5y = 15\]Solve for y:\[y = -3\]So, 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
Understanding the x-intercept is key to analyzing the behavior of linear equations. To find the x-intercept of a linear equation, you set the value of y to zero. This is because the x-intercept appears where the line crosses the x-axis, and at all points on the x-axis, the value of y is zero.
y-intercept
The y-intercept reveals where a line crosses the y-axis. To find the y-intercept of a linear equation, you set the value of x to zero. The y-intercept represents the point where the equation passes through the y-axis, and at this point, the value of x is zero.
solving linear equations
Solving linear equations involves manipulating the equation to find the values of x and y that satisfy it. A linear equation is an equation between two variables that gives a straight line when plotted on a graph. To find the intercepts of the equation, set y to zero to solve for the x-intercept and then set x to zero to find the y-intercept.

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Most popular questions from this chapter

Let \(f(x)=3 x-2, g(x)=-x^{2}+3 x-2,\) and \(h(x)=|x+2|\). Evaluate each expression. See Example 9. $$ f(4) $$

If a certain fabric is priced at \(\$ 3.98\) per yard, express the cost \(C(x)\) as a function of the number of yards \(x .\) Find \(C(3)\).

Let \(f(x)=3 x-2, g(x)=-x^{2}+3 x-2,\) and \(h(x)=|x+2|\). Evaluate each expression. See Example 9. $$ f(0) $$

Find all intercepts for each line. Some of these lines have only one intercept. $$y=-4 x$$

Find the equation of line l in each case and then write it in standard form with integral coefficients. Line \(l\) goes through \((1,-3)\) and is parallel to \(y=-3 x-5\).
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