x y
-2 10
-1 8
0 6
1 4
2 2
3 0
The x and y values given in the table represent points on a linear graph. The equation of the line can be determined by finding the slope and y-intercept.
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
Using the given values, we can calculate the slope between each pair of points:
m1 = (8 - 10) / (-1 - (-2)) = -2 / 1 = -2
m2 = (6 - 8) / (0 - (-1)) = -2 / 1 = -2
m3 = (4 - 6) / (1 - 0) = -2 / 1 = -2
m4 = (2 - 4) / (2 - 1) = -2 / 1 = -2
m5 = (0 - 2) / (3 - 2) = -2 / 1 = -2
The slope remains constant throughout, which means the line is a straight line.
Now, to find the y-intercept (b), we can substitute any of the given points into the slope-intercept form of a line (y = mx + b) and solve for b.
Let's use the point (0, 6):
6 = -2(0) + b
6 = b
Therefore, the y-intercept (b) is 6.
Now that we have the slope (m = -2) and the y-intercept (b = 6), we can write the equation of the line:
y = -2x + 6