Write the linear equation that gives the rule for this table.
X Y
3 20
4 21
5 22
6 23
To find the linear equation that gives the rule for this table, we can observe that the value of Y increases by 1 as X increases by 1. Therefore, we can conclude that there is a constant rate of change of 1.
We can use the point-slope form of a linear equation to find the equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line, and m is the slope.
Let's choose the first point (3, 20):
y - 20 = 1(x - 3)
Simplifying the equation:
y - 20 = x - 3
Now, let's rearrange the equation to solve for y:
y = x - 3 + 20
y = x + 17
Therefore, the linear equation that gives the rule for this table is y = x + 17.
To find the equation for a linear relationship, we need to identify the pattern between the given values of X and Y. In this case, as X increases by 1, Y increases by 1 as well. So, the relationship between X and Y is a constant increase of 1.
To find the equation, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Since the slope is 1 (for each increase in X, Y increases by 1), we have the equation:
y = 1x + b
Now we need to find the value of b. To do this, we can substitute one of the points from the table into the equation. Let's use the point (3, 20):
20 = 1(3) + b
20 = 3 + b
Now, we can solve for b by subtracting 3 from both sides:
20 - 3 = b
b = 17
So, the equation that gives the rule for the table is:
y = x + 17
To determine the linear equation that represents the relationship between the given values in the table, we need to find the equation in the form y = mx + b, where:
- y represents the dependent variable (in this case, Y),
- x represents the independent variable (in this case, X),
- m represents the slope, and
- b represents the y-intercept.
To find the slope (m), we need to calculate the rate of change between any two points from the table. Let's choose the first and second points (3, 20) and (4, 21):
m = (Y2 - Y1) / (X2 - X1)
m = (21 - 20) / (4 - 3)
m = 1 / 1
m = 1
The slope (m) is 1.
Next, we need to find the y-intercept (b). We can choose any point from the table and substitute its values into the equation y = mx + b. Let's use the first point (3, 20) to solve for b:
20 = 1(3) + b
20 = 3 + b
b = 20 - 3
b = 17
The y-intercept (b) is 17.
Therefore, the linear equation that represents the given table is y = x + 17.