Final answer:
The linear equation with an x-intercept at (3/2,0) and y-intercept at (0,9) is y = -6x + 9. The slope is calculated as -6 by using the intercepts to find the change in y over the change in x.
Step-by-step explanation:
To find a linear equation with an x-intercept at (⅔,0) and a y-intercept at (0,9), we can start by understanding the slope-intercept form of a linear equation: y=mx+b, where m is the slope and b is the y-intercept. Given the points for the intercepts, we can calculate the slope m as the rise over the run, which is the change in y over the change in x. Using the intercepts (⅔,0) and (0,9), we find the slope to be:
m = ∂ y / ∂ x = (9 - 0) / (0 - ⅔) = 9 / (-⅔) = -6
Now that we have the slope and the y-intercept (b), we can substitute them into the slope-intercept formula:
y = mx + b
y = (-6)x + 9
The resulting equation of the line with the specified x-intercept and y-intercept, thus, is y = -6x + 9.