The question asks to drag and drop the correct equation:
this kind of questions can solved by two methods:
the first is to find the equation of each line by using the form y = mx + c
this method takes a little more time
The second method using x and y intercepts and showing the rate of change is positive or negative
it is better to use the first method to be sure the solution is correct:
so, lets find the equation for each graph:
Graph A:
using two points to find the equation:
pick the points (0,5) and (3,6)
when x = 0 , y= 5 , so, 5 = 0 * m + c
so, c = 5
y = mx + 5
when x = 3 y = 6
so, 6 = 3m + 5 so, 3m = 1 so, m = 1/3
so, y = (1/3) x + 5
Graph B :
pick the points (0,9) and (1,7)
when x = 0 , y = 9 so, c = 9
when x = 1 , y = 7
7 = m + 9 so, m = 7 - 9 = -2
so, y = -2 x + 9
Graph C :
for this kind of functions, it is constant at y = -3
Graph D:
Pick the points (0,9) and (3,15)
when x = 0 , y = 9 and hence c = 9
when x = 3 , y = 15
so, 15 = 3m + 9
3m = 15 - 9 = 6
m = 6/3 = 2
y = 2x + 9
Graph E:
Using the points (0 , 80) and (2 , 60)
when x = 0 , y = 80 and hence c = 80
when x = 2 , y = 60
so, 60 = 2m + 80
2m = 60 - 80 = -20
m = -10
so, y = -10 x + 80
The final graph D:
using the points (0 , -2) and (2,0)
when x = 0 , y = -2 so, c = -2
when x = 2 , y = 0
so, 0 = 2m - 2
2m = 2
m = 1
so, y = x - 2
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The error of the graph A: y = 30 x + 10
he confused between the slope of the line and y-intercept
as shown y-intercept = 10 and the slope = 30
but on the graph he made y-intercept = 30, and the slope = 10
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The error of the graph B: y = (-1/2) x + 5
the slope of the equation is negative, but he made it positive
because, when we put x = 2 at the equation, the value of y = (-1/2)*2 + 5 = 4
but on the graph at x = 2 , y = 6
which confirm our analysis y = (1/2) * 2 + 5 = 6
so, he forget the minus sign in the front of the slope of the line which is (1/2)
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The error of the final graph:
the given equation is y = x - 2
lets find the equation of the graph using the points (0,2) and (2,0)
using the general form of the line y = mx + c
when x = 0 , y = 2 so, c = 2
when x = 2 , y = 0 so, 0 = 2m + 2
2m = -2 and hence m = -1
so, the equation of the student is y = -x + 2
By comparing the two equations y = x - 2 and y = -x + 2
we can conclude that:
Both of them is reverse to the other
i mean he wrote (-x) instead of (x) and (2) instead of (-2)