Write the linear equation that gives the rule for this table.
X Y
3 24
4 32
5 40
6 48
We can see that as the value of X increases by 1, the value of Y increases by 8. Therefore, the slope of the linear equation is 8.
To find the y-intercept, we can use the point-slope form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Using the point (3, 24), we can substitute the values into the equation:
24 = 8(3) + b
Simplifying, we get:
24 = 24 + b
Subtracting 24 from both sides, we find:
b = 0
Therefore, the linear equation that gives the rule for this table is:
y = 8x + 0
Simplified, the linear equation is:
y = 8x
To find the linear equation that gives the rule for this table, we can observe that as X increases by 1, Y increases by 8. This indicates a constant rate of change.
We can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can take any two points from the table. Let's use (3, 24) and (4, 32):
m = (Y2 - Y1) / (X2 - X1)
= (32 - 24) / (4 - 3)
= 8 / 1
= 8
Now that we have the slope, we can substitute one of the points into the equation to find the y-intercept (b). Let's use (3, 24):
24 = 8(3) + b
24 = 24 + b
b = 0
Therefore, the linear equation that gives the rule for this table is:
y = 8x + 0
or simply:
y = 8x
To find the linear equation that gives the rule for this table, we need to determine the relationship between the x-values and y-values.
Let's look at the y-values in relation to the x-values. Notice that each y-value is 8 more than the previous y-value. We can see this pattern because when we increase the x-value by 1, the y-value increases by 8.
Now we can use this information to determine the equation of the line. Since the y-value increases by 8 when the x-value increases by 1, we can say that the slope (m) of the line is 8.
To find the y-intercept (b) of the line, we can select any point from the table. Looking at the table, we can see that when x = 3, y = 24. So, the y-intercept is 24.
Therefore, the linear equation that gives the rule for this table is:
y = mx + b
Substituting the values we found:
y = 8x + 24