Write an equation of the line that passes through the points in the table.
x 0 1 2 3
y 10 7 4 1
To find the equation of the line that passes through the points (0, 10), (1, 7), (2, 4), and (3, 1), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope, m. The slope is defined as the change in y divided by the change in x. We can pick any two points from the table to calculate the slope. Let's use the first and last points, (0, 10) and (3, 1).
The change in y is 1 - 10 = -9.
The change in x is 3 - 0 = 3.
Therefore, the slope, m, is -9/3 = -3.
Next, let's find the y-intercept, b. Since the equation passes through the point (0, 10), we can substitute these values into the equation y = mx + b and solve for b.
10 = -3(0) + b
10 = b
Therefore, the y-intercept is b = 10.
Now we have the slope, m = -3, and the y-intercept, b = 10. Let's substitute these values back into the slope-intercept form of the equation to find the final equation.
y = mx + b
y = -3x + 10
Therefore, the equation of the line that passes through the given points is y = -3x + 10.