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Chapter 16: Problem 17

The equation of a line that has a slope of \(-2\) and intercepts the \(x\)-axis at \(x=2\) is a) \(y+2 x=4\) b) \(y-2 x=4\) c) \(y+2 x=-4\) d) \(2 y+x=2\)

Short Answer

Expert verified
Answer: a) \(y + 2x = 4\)

Step by step solution

01

Understand the given information

We are given the slope (\(m = -2\)) and x-intercept (\(x = 2\)). To find the y-intercept, we need to remember that at the x-intercept, the value of \(y\) is \(0\). Using this, we can write the equation in the point-slope form: \(y - y_1 = m(x - x_1)\).
02

Substitute the given values into the point-slope form

Replacing the given information in the point-slope form, we get: \(y - 0 = -2(x - 2)\) Simplifying the equation, we get: \(y = -2x + 4\)
03

Compare with the given options

Our equation is \(y = -2x + 4\). Now we need to compare it with the given options to find the correct answer: a) \(y + 2x = 4\) b) \(y - 2x = 4\) c) \(y + 2x = -4\) d) \(2y + x = 2\)
04

Identify the correct option

By comparing our equation with the given options, we can see that option a) matches our equation: \(y = -2x + 4 \Rightarrow y + 2x = 4\). So, the correct answer is: a) \(y + 2x = 4\).

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