NAEP Grade 8 Algebra. Practice it free.

In $y = mx + b$, the $y$-intercept is $b = -6$.

Substitute $x = 7$: $6(7) + k = 30$, so $42 + k = 30$ and $k = -12$. The rule is $v(x) = 6x - 12$, so $v(4) = 6(4) - 12 = 24 - 12 = 12$.

She starts at $\text{\char36}75$ (intercept) and gains $\text{\char36}20$ per week (slope), so $y = 20x + 75\textsf{.}$

Slope $= \dfrac{-5 - 4}{2 - (-1)} = \dfrac{-9}{3} = -3\textsf{.}$

The first equation gives $y = -2x + 5\textsf{.}$ The second simplifies to $y = -2x + 6\textsf{,}$ so the slopes match but the intercepts differ and the system has no solution.

The speed must be at most $35.0$ miles per hour. The minimum decrease is $38.2 - 35.0 = 3.2\textsf{.}$

Rewrite in slope-intercept form: $y = -\dfrac{3}{4}x + \dfrac{5}{2}$ and $y = \dfrac{1}{2}x - \dfrac{1}{2}$. The slopes $-\dfrac{3}{4}$ and $\dfrac{1}{2}$ are different, so the lines intersect at exactly one point.

Distribute $\dfrac{1}{2}$: $2x + 3 + x = 15$. Combine like terms: $3x + 3 = 15$. Subtract $3$ from both sides: $3x = 12$. Divide by $3$: $x = 4\textsf{.}$