Find the equation of a line containing the following points. Write the equation in slope-intercept form.
(2,3) and (2,−2)
My answer:
y= -5x+8
It was easy to check your answer is not correct.
The point (2,3) does not satisfy your equation, neither does (2,-2)
notice that both points have an x value of 2, so you have a vertical line.
The equation of a vertical line has the form x = k, where k is the x of any point on the line. All the x's would have to be the same.
so x = 2 is your equation.
Vertical lines CANNOT be written in the slope-yintercept form, since the slope is undefined.
To find the equation of a line containing two points, we can use the slope-intercept form of a line, which is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (2,3) and (2,-2):
m = (-2 - 3) / (2 - 2)
m = -5 / 0
The slope is undefined since the denominator is zero. This means that the line is vertical.
Since the line is vertical and the x-coordinate is the same for both points, we can simply write the equation as:
x = 2
So the equation of the line in slope-intercept form is x = 2.
To find the equation of a line containing two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line, and b is the y-intercept.
First, let's find the slope (m):
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (2,3) and (2,-2), we have:
m = (-2 - 3) / (2 - 2) = -5 / 0
Since the denominator is 0, this means that the line is vertical and its slope is undefined. Therefore, we cannot represent this line using the slope-intercept form, y = mx + b.
However, we can write the equation of a vertical line in the form x = c, where c is the x-coordinate of any point on the line. In this case, the x-coordinate is 2.
So, the equation of the line containing the points (2,3) and (2,-2) is:
x = 2