Question

1.) Write the point-slope form of the equation of the line with a slope of - 2 and an x-intercept of - 1. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

2.) Write the point-slope form of the equation of the line that passes through the point (1, 3) and has a slope of 2. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
3.) Write the point-slope form of the equation of the line that passes through the point (-1, 5) and has a slope of -1. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
4.) Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
5.) A line passes through the point (-6, 6) and (-6, 2). In two or more complete sentences, explain why it is not possible to write the equation of the given line in the traditional version of the point-slope form of a line. Type your answer in the box provided or use the upload option to submit your solution.

Answer 1

The point-slope form equations for the given slopes and points are presented, demonstrating the application of the slope and a specific point on the line. For the vertical line case, the reason behind the impossibility of representing it in the traditional point-slope form, due to an undefined slope, is explained.

Step-by-step explanation:

1.) The point-slope form of the equation of the line with a slope of -2 and an x-intercept of -1 can be written as y - 0 = -2(x - (-1)) or y = -2(x + 1). Since the line intercepts the x-axis at (-1,0), we can use this point and the slope to write the equation.

2.) For a line passing through (1, 3) with a slope of 2, the point-slope form is given by y - 3 = 2(x - 1).

3.) For a line passing through (-1, 5) with a slope of -1, we use the same format to write the equation as y - 5 = -1(x - (-1)) or y - 5 = -1(x + 1).

4.) A horizontal line passing through (2, 1) has a slope of 0, thus the point-slope form is simply y = 1, since the y-value remains constant.

5.) It is not possible to write the equation of a line passing through (-6, 6) and (-6, 2) in the traditional point-slope form because this line is vertical and the slope is undefined. The x-value remains constant at -6, indicating that there is no run, only a rise or fall, which is why the slope calculation (rise/run) would result in division by zero.