Choose the point-slope form of the equation below that represents the line that passes through the points (−6, 4) and (2, 0).
A y − 4 = −one half(x + 6)
B y − 4 = 2(x + 6)
C y + 6 = −one half(x − 4)
D y + 6 = 2(x − 4)
Well, looking at the options, it seems like the equation is dressing up for a costume party, with y and x playing hide-and-seek. Let's see which equation is their best disguise!
Let's take a look at option A, where y - 4 = -1/2(x + 6). This equation seems to be wearing a clown nose made out of -1/2, which means that the slope of the line is -1/2. Is this the right outfit? Let's check!
Using the given points (−6, 4) and (2, 0), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1).
Using (-6, 4) and (2, 0), we get:
m = (0 - 4) / (2 - (-6))
m = -4 / 8
m = -1/2
Oh my, it seems like option A's clown nose fits perfectly! So, the correct answer is:
A) y - 4 = -1/2(x + 6)
I hope my clown-like explanation brought a smile to your face!
To find the point-slope form of the equation that represents the line passing through the given points (-6, 4) and (2, 0), we can use the formula:
y - y1 = m(x - x1)
Where (x1, y1) represents one of the points and m represents the slope of the line.
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-6, 4) and (2, 0):
m = (0 - 4) / (2 - (-6))
m = -4 / 8
m = -1/2
Now that we have the slope, let's use one of the given options to see if it matches.
Option A: y - 4 = -1/2(x + 6)
Option B: y - 4 = 2(x + 6)
Option C: y + 6 = -1/2(x - 4)
Option D: y + 6 = 2(x - 4)
Plugging the coordinates (-6, 4) into each option, we can see which equation holds true:
Option A: 4 - 4 = -1/2(-6 + 6) --> 0 = 0 (True)
Option B: 0 - 4 = 2(2 + 6) --> -4 = 16 (False)
Option C: 4 + 6 = -1/2(-6 - 4) --> 10 = 5 (False)
Option D: 0 + 6 = 2(2 - 4) --> 6 = -4 (False)
Therefore, the correct point-slope form of the equation representing the line passing through (-6, 4) and (2, 0) is:
A) y - 4 = -1/2(x + 6)
To determine the point-slope form of the equation, we need to use the formula:
(y - y₁) = m(x - x₁),
where m represents the slope of the line and (x₁, y₁) represents the coordinates of one of the points on the line.
Given the points (−6, 4) and (2, 0), let's find the slope first:
m = (y₂ - y₁) / (x₂ - x₁)
m = (0 - 4) / (2 - (-6))
m = -4 / 8
m = -1/2
Now we can substitute one of the points, let's use (−6, 4), into the point-slope formula:
(y - y₁) = m(x - x₁)
(y - 4) = (-1/2)(x - (-6))
y - 4 = (-1/2)(x + 6)
y - 4 = (-1/2)x - 3
y = (-1/2)x + 1
Therefore, the correct answer is A: y − 4 = −one half(x + 6).