Question

Determine the slope and y-intercept of the line represented by the linear equation: 1/2y + 2 = 0. Graph the line using the slope and y-intercept. Describe, in complete sentences, what type of linear relationship the solutions (points) of the line have with each other. Choose two points on the line and prove that they are solutions of the linear equation. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.

Answer 1

1) Attached please find the graph of the equation 1/2·y + 2 = 0

2) The values of the y-coordinates for the points are the same, while the values of the x-coordinate of the points increases as we move from left to right

3) The result of substituting the x values of two points on the line in the equation 1/2·y + 2 = 0, gives y = -4, which proves that they are solutions of the linear equation

Explanation:

1) The given equation is 1/2·y + 2 = 0

Therefore, the given equation in slope and intercept form, y = m·x + c, can be presented as follows;

1/2·y + 2 = 0

1/2·y = 0 - 2 = -2

y = -2 × 2 = -4

y = -4

Therefore, by comparing the above equation with the equation for a straight line, y = m·x + c, we have;

m = 0, c = -4

Therefore, the graph is an horizontal line with y-intercept at (0, -4)

2) The relationship of the solutions (points) on of the line have with each other are;

a) The values of the y-coordinates for the points are the same, while the values of the x-coordinate of the points increases as we move from left to right

3) Two points on the line are the points (3, -4) and (33, -4)

With the slope = 0, the linear equation is given as follows;

y = 0·x - 4

For the point (3, -4) we have;

y = 0×3 - 4 = -4

y = -4

For the point (33, -4) we have;

y = 0×33 - 4 = -4

y = -4

Therefore, the two points are solutions of the linear equation 1/2·y + 2 = 0, where y = -4.