7. 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
The relationship is linear. y – 4 = 1 over 2(x – 3)
The relationship is linear. y = 2 over 2(x + 4)
The relationship is linear. y – 10 = 1 over 2(x – 3)
The relationship is not linear.
assuming your table is:
x: -10, -4, -1, 3
y: -3, 0, 2, 4, and not some kind of absolute value relation,
the slope between pairs of point is ...
(-3-0)/(-10+4) = -3/-6 = 1/2
.. (4-2)/(3+1) = 1/2
but (2-0)/(-1+4) = 2/3
so the relationship is not linear according to my assumption.
If you do imply absolute values, then just make all the data values
positive and test for slope
Furthermore, just type fractions like 2/3 instead of in words.
it's linear if it has a constant slope.
In this case, it's not.
To determine if the relationship shown by the data is linear, we can plot the data points and observe if they form a straight line.
When we plot the given data points on a coordinate plane, we can see that they form a straight line. Therefore, the relationship is linear.
To model the data with an equation, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, m represents the slope, and b represents the y-intercept.
To find the equation of the line, we need to determine the values of m and b. Let's use the point-slope form of a linear equation to find the equation: y – y1 = m(x – x1).
Using the first and second data points (-10, -3) and (-4, 0), we can calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (0 - (-3)) / (-4 - (-10))
= 3 / 6
= 1/2
Now that we have the slope (m), we can substitute one of the data points into the point-slope form equation to find the y-intercept (b). Let's use the first data point (-10, -3):
-3 - (-10) = (1/2)(-10 - x)
-3 + 10 = -5 - (1/2)x
7 = -5 - (1/2)x
7 + 5 = -(1/2)x
12 = -(1/2)x
-24 = x
So, the equation of the line is y = (1/2)x + 12.
Therefore, the correct answer is:
The relationship is linear. y = (1/2)x + 12.
To determine whether the relationship shown by the data is linear, we need to plot the data points on a graph and observe the pattern.
Let's plot the given data points:
(x, y) = (-10, -3), (-4, 0), (-1, 2), (3, 4)
After plotting these points on a graph, if the points form a straight line or show a consistent pattern, then the relationship is linear.
By plotting the points, we can see that they do form a straight line. Therefore, the relationship shown by the data is linear.
Once we establish that the relationship is linear, we can proceed to model the data with an equation.
To find the equation, we can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
Let's choose two points: (-10, -3) and (3, 4).
m = (4 - (-3)) / (3 - (-10)) = 7 / 13
Now that we have the slope, we can substitute it into the equation and solve for the y-intercept, b.
Using the point (3, 4):
4 = (7/13)(3) + b
4 = 21/13 + b
b = 52/13 - 21/13 = 31/13
Therefore, the equation that models the data is:
y = (7/13)x + 31/13