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Chapter 1: Problem 20

If the slope of the line shown is 3 , then what is the \(x\) coordinate of point \(\mathrm{B}\) ? A. -5 B. -3 C. 3 D. 5

Short Answer

Expert verified
The x-coordinate of point B is -3.

Step by step solution

01

Identify the given information

We are given the slope of the line = 3. Also, we know that one point on the line is A(-3, 1) and we need to find the x-coordinate of point B. Let's assume the coordinates of point B are (x, y).
02

Use point slope form of the equation to find the x-coordinate

The point slope form of the equation of a line is given by: (y - y1) = m(x - x1), where m is the slope and (x1, y1) are the coordinates of point A. We have m = 3, and point A has coordinates (-3, 1). Let's substitute the value of m and the coordinates of point A in the point slope equation to find the equation of the line. (y - 1) = 3(x - (-3)) Now we need to find a point on the line, using the possible x-coordinates provided in the options (A to D).
03

Check each option

Let's substitute each potential x-coordinate from the options into our equation and see which one gives us an integer value for y. A) x = -5: (y - 1) = 3(-5 - (-3)) => (y - 1) = 3(-2) => y = -5 B) x = -3: (y - 1) = 3(-3 - (-3)) => (y - 1) = 3(0) => y = 1 C) x = 3: (y - 1) = 3(3 - (-3)) => (y - 1) = 3(6) => y = 19 D) x = 5: (y - 1) = 3(5 - (-3)) => (y - 1) = 3(8) => y = 25
04

Determine the correct x-coordinate

Among the options A to D, only option B gives us an integer value for y when we substitute the x-coordinate into the equation. Thus, the x-coordinate of point B is -3. The correct answer is B) -3.

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