Which of the following represents a linear function with the same slope as the table below? *Select 2 that apply!
(2 points) Responses Cynthia has $200 in her savings account and spends $3 per day on coffee. Cynthia has $200 in her savings account and spends $3 per day on coffee. 6x−2y=12 6 x minus 2 y is equal to 12 James increases his muscle mass by 3 kg per day.
x f(x)
-4 14
-2 8
3 -7
5 -13
The slope of a linear function can be determined by finding the change in the output values (y-values) divided by the change in the input values (x-values). In this case, we can calculate the slope using the data provided:
slope = (change in y)/(change in x)
From the table, we can see that for each increase of 2 in the x-values, the y-values decrease by 6. Therefore, the slope is -6/2 = -3.
Now let's check the given options to see which ones have the same slope:
1. 6x−2y=12: This equation is not in slope-intercept form (y = mx + b), so we can't directly compare the slope without converting it. But by rearranging the equation and isolating y, we can see that the coefficient of x is 6/2 = 3, which is the same as the slope of -3 described in the table. So this equation represents a linear function with the same slope.
2. 6x - 2y = 12: This is the same equation as the previous option, so it also represents a linear function with the same slope.
3. James increases his muscle mass by 3 kg per day: This statement does not provide enough information to determine the slope of a linear function. We do not know the relationship between James's muscle mass and any other variable.
Therefore, the correct options are:
1. 6x−2y=12
2. 6x - 2y = 12
one of ur answers arent correct
Apologies for the incorrect answer. Let's reevaluate the options:
1. 6x−2y=12:
Rearranging the equation, we get:
-2y = -6x + 12
Dividing throughout by -2, we have:
y = 3x - 6
The slope of this equation is 3, which is not the same as the slope in the table (-3). Therefore, this equation does not represent a linear function with the same slope.
2. 6x - 2y = 12:
This is the same equation as the previous option, so it also yields the same result. The slope is 3, which is not the same as the slope in the table (-3). Therefore, this equation also does not represent a linear function with the same slope.
3. James increases his muscle mass by 3 kg per day:
This statement does not provide an equation or any relationship to determine the slope of a linear function. Therefore, it does not apply.
Therefore, none of the provided options represent a linear function with the same slope as the table.