What is the equation of the line that passes through all the points in the table?
x -4 -2 0 2
y 0 -4 -8 -12
A. y= -2x-8
B. y= -2x-4
C. y= -4x-8
D. y= -4x-4
PLEASE EXPLAIN PLZZ
Take two points from the given. For instance the first two points (-4,0) and (-2,-4).
Get the slope using the formula,
m = (y2 - y1) / (x2 - x1)
where
(x1,y1) and (x2,y2) are points on the line.
Substituting,
m = (0 - (-4)) / (-4 - (-2))
m = (0 + 4) / (-4 + 2)
m = 4 / -2
m = -2
Finally substitute the slope and a point in slope-intercept form of equation:
y - y1 = m(x - x1)
y - 0 = -2(x - (-4))
y = -2(x + 4)
y = -2x - 8
hope this helps~ `u`
THANK YOU SM JAI
To determine the equation of the line that passes through all the points in the table, we need to find the slope (m) and the y-intercept (b) of the line.
Step 1: Find the slope (m):
The slope of a line can be determined by using the formula:
m = (change in y) / (change in x)
Let's take two points from the table to calculate the slope:
Point 1: (-4, 0)
Point 2: (0, -8)
Change in y = -8 - 0 = -8
Change in x = 0 - (-4) = 4
So, the slope (m) can be calculated as:
m = (-8) / 4 = -2
Step 2: Find the y-intercept (b):
We can use the slope-intercept form of a linear equation, which is: y = mx + b, where m is the slope and b is the y-intercept.
Taking one point from the table, let's substitute the values into the equation to find the y-intercept:
Using the point (-4, 0):
0 = -2 * (-4) + b
0 = 8 + b
b = -8
Step 3: Write the equation of the line:
Now that we have the slope (m) and the y-intercept (b), we can form the equation of the line:
y = -2x - 8
Comparing this equation with the given answer choices, we can see that the correct equation is:
A. y = -2x - 8