Hi there!
Let me solve your problems step-by-step, so to ensure your understanding.
1. We are asked to find the solutions to the inequality 2y - x ≤ -6. We are given the choices (1, -4), (2, -2), and (-3, 0). All we have to do is plug in the respective values for each coordinate into the given inequality.
a. (1, -4)
2(-4) - 1 ≤ -6
-8 - 1 ≤ -6
-9 ≤ -6
Since -9 ≤ 6 is a true statement, (1, -4) is a solution to the inequality.
b. (2, -2)
2(-2) - 2 ≤ 6
-4 - 2 ≤ 6
-6 ≤ -6 ←This is a true statement, so (2, -2) is a solution to the inequality.
c. (-3,0)
2(0) - (-3) ≤ -6
0 + 3 ≤ -6
3 ≤ -6 ←This is not a true statement, so (-3, 0) is not a solution to the inequality.
Therefore, the answer to number one is A) (1, -4) and B) (2, -2).
2. The question is asking us to write a point-slope equation of a line that has a slope of 2/5 and goes through the point (-4, -7). Point-slope form goes as follows - y - y₁ = m(x - x₁). When we let m = 2/5, y₁ = -7, and x₁ = -4, we can plug the values back in and simplify. Hence, the answer is y + 7 = 2/5( x + 4).
3. We are asked to write a set of constraints or inequalities to model the problem. Here is what we should do to get our answer -
Let x represent the number of lawns mowed
Let y represent the number of dogs walked
Using the first few sentences, we can create a simple inequality.
(price for Jacob)x + (price for Sarah)y ≥ 1975
→ 25x + 15y ≥ 1975
We're not done yet, we are given more information. We are given that Sarah scheduled no more than 4 times the number of lawns Jake has to mow.
This gives us:
y ≤ 4x
Finally, we are given that Sarah will at least walk 50 dogs. Therefore,
y ≥ 50
Our answer will be:
25x + 15y ≥ 1975
y ≤ 4x
y ≥ 50
4. Question is same as Question 1.
Hope this helped and have a phenomenal day!
