Question

plot the points (1,0), (1, - 4), (1,4), (1,8), and (1, - 6). describe the set of all points of the form (1,y), where y is a real number.
plot the point (1,0).
plot the point (1, - 4).
plot the point (1,4).
plot the point (1,8).
plot the point (1, - 6).
describe the set of all points of the form (1,y), where y is a real number.
a. the points are on a horizontal line 1 unit above the x - axis.
b. the points are on a horizontal line 1 unit below the x - axis.
c. the points are on a vertical line 1 unit to the right of the y - axis.
d. the points are on a vertical line 1 unit to the left of the y - axis.

Explanation:

Step1: Recall coordinate - plane concept

In a two - dimensional coordinate plane, a point is represented as $(x,y)$. For points of the form $(1,y)$, the $x$ - coordinate is fixed at $x = 1$ and the $y$ - coordinate can take any real - number value.

Step2: Analyze vertical and horizontal lines

A horizontal line has the equation $y = k$ (where $k$ is a constant) and a vertical line has the equation $x = k$. Since $x = 1$ for the points $(1,y)$, these points lie on a vertical line.

Step3: Determine the position of the vertical line

The value of $x=1$ means the line is 1 unit to the right of the $y$ - axis.

Answer:

C. The points are on a vertical line 1 unit to the right of the y - axis.