Marcus plotted the points (0,0),(6,2),(18,6), and (21,7) on a graph. He wrote an equation for the relationship. Find another ordered pair that could be a solution of Marcus's equation.
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To find another ordered pair that could be a solution of Marcus's equation, we first need to determine the equation of the relationship represented by the given points.
Since Marcus plotted the points (0,0), (6,2), (18,6), and (21,7), we can assume that these points lie on a straight line.
To determine the equation of this line, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
To find the slope (m) of the line, we can choose any two points from the given set of points and use the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose the points (0,0) and (6,2) as our reference points:
m = (2 - 0) / (6 - 0)
= 2 / 6
= 1/3
Now that we have the slope, we can substitute one of the points (0,0), (6,2), or (18,6) into the slope-intercept form equation and solve for the y-intercept (b). Let's use the point (0,0):
0 = (1/3) * 0 + b
0 = 0 + b
b = 0
Therefore, the equation that represents the relationship between the given points is:
y = (1/3)x
Now, we can use this equation to find another ordered pair. We can choose any x-value and calculate the corresponding y-value using the equation. Let's choose x = 9 as an example:
y = (1/3)(9)
y = 3
Therefore, the ordered pair (9, 3) could be another solution of Marcus's equation.
The equation for this relationship is a linear equation (I even used linear regression to prove it lol).
To get the linear equation, we can look for the slope first.
m = (y2 - y1) / (x2 - x1)
where (x1,y1) and (x2,y2) are points on the line.
Taking two points, for instance, (0,0) and (6,2),
m = (2-0) / (6-0)
m = 2/6
m = 1/3
Then we plug in this value in the slope-intercept form:
y - y1 = m(x - x1)
Substituting,
y - 0 = 1/3(x - 0)
y = (1/3)x
Getting another point, for instance, for x = 1,
y = (1/3)(1)
y = 1/3
Therefore the point (1 , 1/3) is also a point on the line.
hope this helps~ `u`