The line drops 4 units between the points (1, 6) and (6, 2) as it goes over 5 units. Thus the point-slope form of the equation can be written as
... y - k = m(x - h) . . . . . . line with slope m through point (h, k)
... y - 6 = (-4/5)(x - 1)
Multiplying by 5 and subtracting the right side gives ...
... 5y - 30 = -4x +4
... 4x + 5y - 34 = 0 . . . . . equation in general form
Answer:
x < -5 or x = 1 or 2 < x < 3 or x > 3
Step-by-step explanation:
Given <u>rational inequality</u>:
Therefore:
Find the roots by solving f(x) = 0 (set the numerator to zero):
Find the restrictions by solving f(x) = <em>undefined </em>(set the denominator to zero):
Create a sign chart, using closed dots for the <u>roots</u> and open dots for the <u>restrictions</u> (see attached).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Test values: -6, 0, 1.5, 2.5, 4
For each test value, determine if the function is positive or negative:
Record the results on the sign chart for each region (see attached).
As we need to find the values for which f(x) ≥ 0, shade the appropriate regions (zero or positive) on the sign chart (see attached).
Therefore, the solution set is:
x < -5 or x = 1 or 2 < x < 3 or x > 3
As interval notation:
