Draw the line through the point (4,5)that is parallel to the y-axis. Write the equation of this line and state its slope.

Can anyone assist me. The example or instructions is not in my text.

think about it. The y-axis has equation

x=0

so, any line parallel to the y-axis, say, c units away, will have the equation

x = c

Your point is (4,5), so the line you want is

x = 4

Its slope is undefined, since x never changes. The line is vertical.

Sure! I'd be happy to assist you.

To draw a line parallel to the y-axis that passes through the point (4, 5), we need to remember that any line parallel to the y-axis is vertical. A vertical line has an undefined slope because the slope of a line is defined as the change in y divided by the change in x, and in the case of a vertical line, the change in x is zero.

To draw this line on a graph, start with the point (4, 5) as your reference. Draw a perfectly vertical line passing through this point. This line will have the same x-coordinate for every point on it.

Since the line is parallel to the y-axis and passes through the point (4, 5), the equation of the line can be written as x = 4. This equation means that the x-coordinate will always be 4, regardless of the value of y.

In summary:
- The equation of the line parallel to the y-axis passing through the point (4, 5) is x = 4.
- The slope of this line is undefined because it is a vertical line.

I hope this helps! Let me know if you have any further questions.