Let's go through each question step by step.

Question 1: Identify the slope and y-intercept in $y = \frac{4}{5}x - 9$.

In the equation $y = mx + b$:

• $m$ (slope) = $\frac{4}{5}$
• $b$ (y-intercept) = -9

Answer: m = $\frac{4}{5}$, b = -9 (First option).

Question 2: Find the slope between points (4, 10) and (7, 18).

The slope $m$ is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18 - 10}{7 - 4} = \frac{8}{3}$

Answer: $\frac{8}{3}$ (Second option).

Question 3: Find the x-intercept of $2x + 4y = 28$.

To find the x-intercept, set $y = 0$: $2x + 4(0) = 28 \implies 2x = 28 \implies x = 14$ Thus, the x-intercept is $(14, 0)$.

Answer: (14, 0) (Fourth option).

Question 4: Is the ordered pair (3, 5) a solution for $3x + 6 = y$?

Substituting $x = 3$: $3(3) + 6 = 9 + 6 = 15 \quad \text{and} \quad y = 5$ Since $15 \neq 5$, the ordered pair is not a solution.

Answer: False.

Question 5: Identify the slope and y-intercept in $y = 4 - \frac{2}{5}x$.

Rewriting it in slope-intercept form $y = mx + b$: $y = -\frac{2}{5}x + 4$ Thus, $m = -\frac{2}{5}$ and $b = 4$.

Answer: m = -$\frac{2}{5}$, b = 4 (Third option).

Summary of Answers:

1. m = $\frac{4}{5}$, b = -9
2. $\frac{8}{3}$
3. (14, 0)
4. False
5. m = -$\frac{2}{5}$, b = 4

Do you want details or have any questions? Here are some related questions for further exploration:

1. How would you graph the equation $y = \frac{4}{5}x - 9$?
2. What is the significance of the slope in a linear equation?
3. How can you find the y-intercept from a standard form equation?
4. What do the coordinates of an x-intercept represent?
5. How can you determine if a point is a solution for any linear equation?

Tip: Always write equations in slope-intercept form to easily identify slope and y-intercept.