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.