x, y
4, 38
6, 58
Write the equation of the linear function that models the relationship shown in the table.
1. y = 10x − 2
2. y = x + 34
3. y = 10 x + 2
4. y = − 10x + 78
Since the relationship shown in the table is linear, we can use the two data points to find the slope of the line.
slope (m) = (change in y)/(change in x)
= (58-38)/(6-4)
= 20/2
= 10
Now we can use the slope and one of the data points to find the y-intercept (b) using the slope-intercept form of the equation for a line:
y = mx + b
We can use (4, 38) as our data point:
38 = 10(4) + b
b = -2
So the equation of the linear function that models the relationship shown in the table is:
y = 10x - 2
Therefore, the correct answer is 1. y = 10x − 2.
To find the equation that models the relationship shown in the table, we need to use the formula for the equation of a linear function, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Looking at the given values, we can see that as x increases by 2, y increases by 20. This means the slope, m, is 20/2 = 10.
To find the y-intercept, we can substitute one of the x and y values into the equation and solve for b.
Using the values (4, 38), we have 38 = 10(4) + b. Solving for b, we get b = 38 - 40 = -2.
Therefore, the equation of the linear function that models the relationship shown in the table is y = 10x - 2, which is option 1.