Question

is the relationship shown by the data Linear? if it is model the data with an equation x: -10, -4, -1, 3 Y: -3, 0, 2, 4 1. The relationship in linear. y-4=1 over2(x-3) 2. The relationship in linear y=2 over 2(x+4) 3. The relationship is linear y-10=1 over 2(x-3) 4. the relationship is not linear.

Answer 1

To determine if the relationship is linear, we can plot the data points and see if they form a straight line.

The data points are:
(-10, -3)
(-4, 0)
(-1, 2)
(3, 4)

When we plot these points, we can see that they do form a straight line, indicating that the relationship is indeed linear.

To model the data with an equation, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

First, we can calculate the slope using two of the data points:
m = (4 - 2) / (3 - (-1)) = 2 / 4 = 0.5

Next, we can substitute one of the points into the equation to find the y-intercept:
0 = 0.5(-4) + b
0 = -2 + b
b = 2

Therefore, the equation that models the data is:
y = 0.5x + 2