Given that y is directly proportional to x and that y=30 when x=4. a) Find an equation in terms of x and y. b) Determine the value of y when x = 2/3. 7. Solve a) -2(x-3) <= 7-5x, and represent your so

where $k$ is the constant of proportionality.

The final answer is $\boxed{y = \frac{15}{2}x}$.

b) Determine the value of $y$ when $x = \frac{2}{3}$.

The final answer is $\boxed{5}$.

7. Solve

a) $-2(x-3) \le 7-5x$, and represent your solution on the real number line.

The solution is $\boxed{x \le \frac{1}{3}}$.

To represent $x \le \frac{1}{3}$ on a number line, draw a closed circle at $\frac{1}{3}$ and shade the line to the left of $\frac{1}{3}$.

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                   1/3

b) $|2x-5| = 3$

Case 1: $2x - 5 = 3$
Case 2: $2x - 5 = -3$

The solutions are $\boxed{x=4 \text{ or } x=1}$.

8. Given that $\vec{OP} = (a+5)\mathbf{i} + 2\mathbf{j}$ and $\vec{OQ} = 2a\mathbf{i} - 2\mathbf{j}$, where $a$ is a constant.

a) Find $\vec{PQ}$ in terms of $a$.

The final answer is $\boxed{(a - 5)\mathbf{i} - 4\mathbf{j}}$.

b) When $\vec{PQ} = 3\mathbf{i} - 4\mathbf{j}$, find $a$.

(The $\mathbf{j}$ components, $-4 = -4$, are consistent.)
The final answer is $\boxed{8}$.