What is the slope of the line represented by the points in the table?
x
y
–2
–0.35
–1
–0.3
0
–0.25
1
–0.2
2
–0.15
Negative 0.05
Negative .005
0.005
0.05
The slope of the line is:
m = ∆y / ∆x
In this case:
m = ( y2 - y1 ) / ( x2 - x1 )
m = [ - 0.3 - ( - 0 .35 ) ] / [ - 1 - ( - 2 ) ]
m = ( - 0.3 + 0 .35 ) / ( - 1 + 2 )
m = 0.05 / 1
m = 0.05
m = ( y3 - y2 ) / ( x3 - x2 )
m = [ - 0.25 - ( - 0 .3 ) ] / [ 0 - ( - 1 ) ]
m = ( - 0.25 + 0 .3 ) / ( 0 + 1 )
m = 0.05 / 1
m = 0.05
m = ( y4 - y3 ) / ( x4 - x3 )
m = [ - 0.2 - ( - 0 .25 ) ] / ( 1 - 0 )
m = ( - 0.2 + 0 .25 ) / 1
m = 0.05 / 1
m = 0.05
m = ( y5 - y4 ) / ( x5 - x4 )
m = [ - 0.15 - ( - 0 .2 ) ] / ( 2 - 1 )
m = ( - 0.15 + 0 .2 ) / 1
m = 0.05 / 1
m = 0.05
To find the slope of the line represented by the points in the table, we need to calculate the change in y divided by the change in x.
Using the given values, let's calculate the slope using two sets of points.
1) Using the points (-2, -0.35) and (-1, -0.3):
Change in y = (-0.3) - (-0.35) = 0.05
Change in x = (-1) - (-2) = 1
Slope = Change in y / Change in x = 0.05 / 1 = 0.05
Therefore, the slope for this pair of points is 0.05.
2) Using the points (1, -0.2) and (2, -0.15):
Change in y = (-0.15) - (-0.2) = 0.05
Change in x = (2) - (1) = 1
Slope = Change in y / Change in x = 0.05 / 1 = 0.05
Therefore, the slope for this pair of points is also 0.05.
Since both pairs of points give us the same slope, we can conclude that the slope of the line represented by the points in the table is 0.05.
To find the slope of a line represented by the points in the table, you can use the formula for slope:
slope = (change in y)/(change in x)
First, let's identify two points on the line from the table. A good choice would be any two consecutive points.
Let's take the points (-2, -0.35) and (-1, -0.3) as our two points.
Now, we can calculate the change in y and the change in x using the coordinates of these two points.
Change in y = (-0.3) - (-0.35) = 0.05
Change in x = (-1) - (-2) = 1
Plugging these values into the slope formula:
slope = (0.05)/(1) = 0.05
Therefore, the slope of the line represented by the points in the table is 0.05.