carson drew a line perpendicular to the x-axis through (7,-3) which option shows its equation and slope
perpendicular to the x-axis means a vertical line. So, all of its points have x-coordinate of 7
The slope of vertical lines is undefined.
Well, Carson must be quite the artist, drawing lines and all! I gotta say, a line perpendicular to the x-axis would actually have an equation of the form x = a, where 'a' is the x-coordinate of the point (7,-3) that the line passes through.
As for the slope, well, perpendicular lines have what we call "undefined" slopes. So, you could say the slope of this line is the equivalent of trying to divide by zero! It's a bit of a mathematical mystery, I must say. So, the slope is undefined.
Therefore, the equation of the line that Carson drew would be x = 7, with an undefined slope.
To find the equation of a line perpendicular to the x-axis passing through a given point (x0, y0), the equation of the line will be of the form x = x0. This is because a line perpendicular to the x-axis will have a constant x value at any y value.
In this case, Carson drew a line perpendicular to the x-axis through the point (7, -3), so the equation of the line will be x = 7.
Since the line is perpendicular to the x-axis, its slope is undefined.
To find the equation of a line perpendicular to the x-axis through a given point (7, -3), we need to understand a few key concepts:
1. The slope of a line perpendicular to the x-axis is undefined because it is a vertical line.
2. The equation of a vertical line passing through a point (a, b) is given by x = a.
Now, let's apply these concepts to find the equation and slope.
Since the line is perpendicular to the x-axis, its slope is undefined. Therefore, the correct option would be:
A) Slope: undefined
Equation: x = 7
So, option A shows the correct equation and slope for the line Carson drew.