Given the table for x, lawns mowed, and y, money earned:

Question

x - # of lawns mowed 7 6 2 9 3
y - $ earned 294 252 84 378 126

what is the Slope-intercept form

Answer 1

To find the slope-intercept form of the linear equation represented by the data in the table, we first need to calculate the slope (m) and the y-intercept (b).

We will use the formula for slope:
m = (y2 - y1) / (x2 - x1)

Let's calculate the slope using points (x1, y1) = (2, 84) and (x2, y2) = (9, 378):

m = (378 - 84) / (9 - 2)
m = 294 / 7
m = 42

Now that we have the slope, let's calculate the y-intercept (b) by using one of the points from the table in the equation y = mx + b:

Using the point (2, 84) and the slope (m = 42):
84 = 42(2) + b
84 = 84 + b
b = 0

Now we have the slope (m = 42) and the y-intercept (b = 0), so we can write the linear equation in slope-intercept form:

y = 42x + 0
y = 42x

Therefore, the slope-intercept form of the linear equation is y = 42x.

Answer 2

so what's the point- slope form

Answer 3

The point-slope form of the linear equation can be written as:

y - y1 = m(x - x1)

Using the slope (m = 42) and a point from the table (x1, y1) = (2, 84), we can substitute these values into the point-slope form:

y - 84 = 42(x - 2)

Now, simplify the equation:

y - 84 = 42x - 84

Therefore, the point-slope form of the linear equation is y - 84 = 42x - 84.