Identify the slope and y-intercept of the following table values.
x 5,10,15,20,25
y -80,-40,0,40,80
Do you know what slope and y intercept is?
To find the slope and y-intercept of the given table values, we need to use the formula for the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
First, we need to find the slope. The slope (m) can be calculated using the formula:
m = (change in y) / (change in x)
Let's calculate the changes in y and x:
change in y = 80 - (-80) = 160
change in x = 25 - 5 = 20
Using the formula, we can now calculate the slope:
m = 160 / 20
m = 8
So, the slope (m) of the given table values is 8.
Next, we need to find the y-intercept (b). To do this, we can substitute the values of one of the (x, y) points into the equation and solve for b.
Let's use the first point (5, -80):
y = mx + b
-80 = 8(5) + b
-80 = 40 + b
To isolate b, we subtract 40 from both sides:
b = -80 - 40
b = -120
So, the y-intercept (b) of the given table values is -120.
Therefore, the slope is 8 and the y-intercept is -120.
To find the slope and y-intercept of the given table values, we need to analyze the pattern of the points.
First, let's pair the values of x and y:
(x, y)
(5, -80)
(10, -40)
(15, 0)
(20, 40)
(25, 80)
The slope (m) of a line represents the rate of change between two points. It can be calculated using the formula:
m = (change in y) / (change in x)
Let's calculate the change in y and change in x between each pair of points:
For the first pair (5, -80) and (10, -40):
change in y = -40 - (-80) = 40
change in x = 10 - 5 = 5
For the second pair (10, -40) and (15, 0):
change in y = 0 - (-40) = 40
change in x = 15 - 10 = 5
For the third pair (15, 0) and (20, 40):
change in y = 40 - 0 = 40
change in x = 20 - 15 = 5
For the fourth pair (20, 40) and (25, 80):
change in y = 80 - 40 = 40
change in x = 25 - 20 = 5
We notice that the change in y and change in x remain constant for each pair. Since they are all equal to 40/5 = 8, we can conclude that the slope (m) of the line is 8.
Now, let's find the y-intercept (b) of the line. The y-intercept is the value of y when x is equal to zero. From the given table, we don't have a point where x is equal to zero. However, we can still find the y-intercept using the slope and one point from the table.
Let's choose the point (5, -80) to find the y-intercept:
y = mx + b
-80 = 8(5) + b
-80 = 40 + b
b = -120
Therefore, the slope is 8 and the y-intercept is -120.