3 points each: 1 for trying, 1 for showing your work or explaining, and 1 for the correct answer:
1: Graph the Line: Slope = - 2/5, point (-3, 6)
2: Solve for n: 12 - 5(2n + 9) = 3n + 2(n+6)
3: Solve for w: t + zw = r
4: f(x) = 8x + 3; find f(t+2)
5: Jennifer's age is 7 years less than 3 times her daughter's age. The sum of their ages is 57.
How old is Jennifer? How old is her daughter?
1.
- The equation of a line in point-slope form is (y - y1) = m(x - x1), where (x1, y1) is the given point and m is the slope.
- Plugging in the values, we get (y - 6) = (-2/5)(x + 3)
- Rearranging to slope-intercept form, we get y = (-2/5)x + (12/5)
- The graph has a slope of -2/5 and passes through the point (-3, 6).
2.
12 - 5(2n + 9) = 3n + 2(n + 6)
12 - 10n - 45 = 3n + 2n + 12
-10n - 33 = 5n + 12
-10n - 5n = 12 + 33
-15n = 45
n = -3
3.
t + zw = r
Subtract t from both sides: zw = r - t
Divide by z: w = (r - t)/z
4.
f(t+2) = 8(t+2) + 3
f(t+2) = 8t + 16 + 3
f(t+2) = 8t + 19
5.
Let J be Jennifer's age and D be her daughter's age.
J = 3D - 7
J + D = 57
Substitute the first equation into the second:
3D - 7 + D = 57
4D - 7 = 57
4D = 64
D = 16
Substitute D back in to find J:
J = 3(16) - 7
J = 48 - 7
J = 41
Jennifer is 41 years old and her daughter is 16 years old.