Find the equation that represents the linear function described in the table below. What are the x- and y-intercepts?
x values / -8, -4, 4, 6, 12
y values / -4, -3, -1, -0.5, 1
P1(-8, -4), P2(-4, -3).
m = (-3-(-4))/(-4-(-8)) = 1/4.
Y = mx + b.
-4 = (1/4)*(-8) +b,
b = -2. = Y-int.
Eq: Y = (1/4)x - 2.
0 = (1/4)x - 2.
X = 8 = x-int.
To find the equation that represents a linear function from a table, we need to find the slope and the y-intercept.
1. First, let's calculate the slope (m) using the formula:
m = (change in y) / (change in x)
From the table, we can choose two points, for example (-8, -4) and (12, 1), to calculate the slope:
m = (1 - (-4)) / (12 - (-8))
= 5 / 20
= 1/4
So, the slope (m) is 1/4.
2. Next, let's find the y-intercept (b). We can choose any point from the table and solve for b using the formula:
y = mx + b
Let's use the point (-8, -4) to find b:
-4 = (1/4)(-8) + b
-4 = -2 + b
b = -4 + 2
b = -2
So, the y-intercept (b) is -2.
3. Finally, we can write the equation of the linear function in slope-intercept form (y = mx + b):
y = (1/4)x - 2
Now, to find the x-intercept, we set y = 0 and solve for x:
0 = (1/4)x - 2
(1/4)x = 2
x = 2 * 4
x = 8
So, the x-intercept is 8.
Therefore, the equation that represents the linear function is y = (1/4)x - 2, with x-intercept at 8 and y-intercept at -2.
To find the equation that represents the linear function, we need to identify the slope (m) and the y-intercept (b).
First, let's calculate the slope (m) using the formula:
m = (change in y) / (change in x)
For the given table, let's choose two points, (-4, -3) and (12, 1), to determine the slope:
m = (1 - (-3)) / (12 - (-4))
= 4 / 16
= 1/4
Now, we can use the slope-intercept form of a linear equation, y = mx + b, and substitute the calculated slope (1/4) and one of the points, (-4, -3), to solve for the y-intercept (b).
-3 = (1/4)(-4) + b
-3 = -1 + b
b = -2
Therefore, the equation that represents the linear function is y = (1/4)x - 2.
To find the x-intercept, we need to substitute y = 0 into the equation and solve for x:
0 = (1/4)x - 2
(1/4)x = 2
x = 8
Hence, the x-intercept is 8.
The y-intercept can be found by substituting x = 0 into the equation:
y = (1/4)(0) - 2
y = -2
Therefore, the y-intercept is -2.