Write a linear equation relating x and y
x 0 3 6 10
y 2 8 14 22
check y=2x+2
To find a linear equation that relates the values of x and y, we need to identify the pattern between the two sets of numbers. Looking at the values given:
When x is 0, y is 2.
When x is 3, y is 8.
When x is 6, y is 14.
When x is 10, y is 22.
We can observe that as x increases by 3, y increases by 6. This indicates a constant rate of change.
Using this information, we can determine the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
First, let's find the slope:
slope = (change in y) / (change in x)
slope = (22 - 2) / (10 - 0)
slope = 20 / 10
slope = 2
Now, we can find the y-intercept by substituting the values of x, y, and the slope into the equation:
y = mx + b
2 = 0 * 2 + b
2 = b
Therefore, the linear equation relating x and y can be written as:
y = 2x + 2
To write a linear equation relating x and y, we need to find the equation of the line that passes through the given points. To do this, we can use the slope-intercept form of a linear equation, which is commonly represented as y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
Let's calculate the change in y and change in x:
For the points (0, 2) and (3, 8):
(change in y) = 8 - 2 = 6
(change in x) = 3 - 0 = 3
So, the slope (m) = 6 / 3 = 2
Now, let's find the y-intercept (b) by substituting one of the given points into the equation:
Using the point (0, 2):
2 = 2(0) + b
2 = b
Therefore, the y-intercept (b) is 2.
Now we have the slope (m) and the y-intercept (b). We can write the linear equation:
y = 2x + 2
So, the linear equation that relates x and y is y = 2x + 2.