The graph of the line through (2,3) that is perpendicular to the line with equation y= -1 also goes through which point?

(1,4)

(2,-4)
(-2,3)

Think about the line y=-1. What does it look like?

It's all the points where y is -1: (0, -1), (2, -1), (-2000, -1)... so it's a line straight up and down. Any line perpendicular to is must be straight across, so it must be of the form
x = something, where all the values of x are the same.

You know that the perpendicular passes through (2,3). What is the x value of that point?

So which of your choices has the same x-value?

Well, if we have a line perpendicular to y = -1, that means it has a slope that is the negative reciprocal of -1. The slope of the line y = -1 is 0. So, the slope of our perpendicular line would be undefined (since the negative reciprocal of 0 is, well, not a real number).

To find a line with an undefined slope that passes through the point (2,3), we would need to look for a vertical line. Vertical lines have an equation of the form x = a, where a is a constant. So, the point (2,3) lies on the line x = 2.

Therefore, the graph of the line through (2,3) that is perpendicular to y = -1 also goes through the point (2,3). So, the answer is (2,3).

Now, if you'll excuse me, I'm off to juggle some equations! 🤡✨

To find the point where the perpendicular line goes through, we need to first determine the slope of the given line.

The equation of the given line is y = -1, which is in the form y = mx + b, where m represents the slope of the line. So, the slope of the given line is -1.

To find the slope of a line perpendicular to another line, we need to take the negative reciprocal of the slope of the given line.

The negative reciprocal of -1 is 1.

Now we have the slope of the perpendicular line, which is 1.

Next, we can use the point-slope form of a linear equation to find the equation of the perpendicular line.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

We are given the point (2,3) on the perpendicular line, and we know the slope is 1.

Therefore, the equation of the perpendicular line is:

y - 3 = 1(x - 2)

To find the point where this line also goes through, we can substitute the x and y coordinates of the given points into this equation.

Using (1,4):

4 - 3 = 1(1 - 2)
1 = -1, which is not true.

Using (2,-4):

-4 - 3 = 1(2 - 2)
-7 = 0, which is not true.

Using (-2,3):

3 - 3 = 1(-2 - 2)
0 = -4, which is not true.

None of the given points satisfy the equation of the perpendicular line. Therefore, none of the given points lie on the graph of the line that is perpendicular to the line with equation y = -1.

To find the point through which the line passes, we need to consider the equation of the line that is perpendicular to the line with equation y = -1.

The equation y = -1 represents a horizontal line parallel to the x-axis. A line perpendicular to this line would be a vertical line parallel to the y-axis. Since it passes through the point (2,3), it means the x-coordinate remains the same for this perpendicular line.

Therefore, the line passing through (2,3) and perpendicular to the line y = -1 would have the equation x = 2.

To determine which point the line also passes through, we can substitute x = 2 into the given options:

For (1,4):
When x = 2, the y-coordinate is not 4, so (1,4) is not on the line x = 2.

For (2,-4):
When x = 2, the y-coordinate is not -4, so (2,-4) is not on the line x = 2.

For (-2,3):
When x = 2, the y-coordinate remains 3, so (-2,3) is on the line x = 2.

Therefore, the graph of the line through (2,3) that is perpendicular to the line with equation y = -1 also goes through the point (-2,3).