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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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