Write the equation for the linear equation:
x-5 10 15 20 25 30
y-20 30 40 50 50 50
To find the equation for a linear equation, we need to identify the slope (m) and the y-intercept (b) using the given data points.
We are given two points from the table: (10, 30) and (30, 50). We can use these two points to calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose the first point (10, 30) as (x1, y1) and the second point (30, 50) as (x2, y2):
m = (50 - 30) / (30 - 10)
m = 20 / 20
m = 1
Now that we have the slope (m), we can find the y-intercept (b) using the formula:
b = y - mx
Let's choose one of the given points, such as (10, 30), and plug in the values:
30 = 1 * 10 + b
30 = 10 + b
To isolate the variable "b," we subtract 10 from both sides:
30 - 10 = b
20 = b
Now we have the slope (m = 1) and the y-intercept (b = 20). Hence, the equation for the linear equation is:
y = mx + b
Plugging in the values, we get:
y = 1x + 20
Therefore, the equation for the linear equation is: y = x + 20.