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Chapter 1: Problem 62

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ -2 x-8 y+24=0 $$

Short Answer

Expert verified
The x-intercept is found by setting \(y = 0\) in the equation, which yields \(x = 12\). The x-intercept is (12, 0). The y-intercept is found by setting \(x = 0\) in the equation, which yields \(y = 3\). The y-intercept is (0, 3). To sketch the line, plot these points and draw a straight line passing through them.

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y = 0 and solve the equation for x: $$ -2x - 8(0) + 24 = 0 $$ Simplify the equation: $$ -2x + 24 = 0 $$ Now, solve for x: $$ x = \frac{24}{2} = 12 $$ The x-intercept is thus (12, 0).
02

Find the y-intercept

To find the y-intercept, set x = 0 and solve the equation for y: $$ -2(0) - 8y + 24 = 0 $$ Simplify the equation: $$ -8y + 24 = 0 $$ Now, solve for y: $$ y = \frac{24}{8} = 3 $$ The y-intercept is thus (0, 3).
03

Sketch the line

Now that we have the x-intercept (12, 0) and the y-intercept (0, 3), we can sketch the line. Plot the two points on a graph, and then draw a straight line that passes through them. That line represents the straight line defined by the given linear equation: $$ -2x - 8y + 24 = 0 $$

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Most popular questions from this chapter

Write the equation in the slopeintercept form and then find the slope and \(y\) -intercept of the corresponding line. $$ 2 x-3 y-9=0 $$

At a unit price of \(\$ 55\), the quantity demanded of a certain commodity is 1000 units. At a unit price of \(\$ 85\), the demand drops to 600 units. Given that it is linear, find the demand equation. Above what price will there be no demand? What quantity would be demanded if the commodity were free?

Find an equation of the line that satisfies the given condition. Given that the point \(P(2,-3)\) lies on the line \(-2 x+k y+\) \(10=0\), find \(k\)

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