I need help writing the equation of the line passing through the given pairs of points, writing in a slope-intercept form
1. (-1,3) and (4,-2)
2. (2,-3) and (2,4)
first you have to find the slope of the line by using the slope formula. you would do -2-3 over 4-(-1)
the slope is 5/4
then you need to pluge the slope into slope intercept form y=mx+b
(-1/6,-4/7) and (1/6,-3/7) find the slope of the line through
the pair of points.
To write the equation of a line passing through two given points in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Let's start with the first pair of points (-1,3) and (4,-2):
1. Find the slope (m):
The formula to calculate the slope between two points is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points, the slope can be calculated as:
m = (-2 - 3) / (4 - (-1))
m = -5 / 5
m = -1
2. Find the y-intercept (b):
Now that we have the slope (m), we can use one of the given points (-1,3) to find the y-intercept (b).
Plug in the values of one of the points (-1 for x and 3 for y) and the slope (-1 for m) into the slope-intercept form: y = mx + b, and solve for b.
3 = (-1)(-1) + b
3 = 1 + b
b = 3 - 1
b = 2
Now that we have the slope (m = -1) and the y-intercept (b = 2), we can write the equation of the line passing through the given points:
y = -x + 2
Now let's move on to the second pair of points (2,-3) and (2,4):
1. Find the slope (m):
Using the formula mentioned above, the slope between the two points is:
m = (4 - (-3)) / (2 - 2)
m = 7 / 0
Note: The denominator is zero, indicating that the slope is undefined. This means that the line is vertical, and the equation of a vertical line in slope-intercept form cannot be written. However, we can express it as x = a, where a is the x-coordinate shared by both points. In this case, x = 2.
Therefore, the equation of the line passing through the second pair of points is x = 2.