Answer:
Option D) All of the above.
Step-by-step explanation:
Given the two points on the graph:
Let (x1, y1) = (0, 3)
(x2, y2) = (4, 0)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = (0 - 3)/(4 - 0)
m = -¾
Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. Looking at the graph, the line crosses at point (0, 3), which happens to be one of the points we used in solving for the slope. Its y-coordinate is the value of b.
Therefore, the linear equation of the graph is y = -¾ + 3, which matches Option C.
Test Option A:
We need to determine whether Option A is also a correct answer. Transform the equation into its slope-intercept form:
y - 6 = -¾(x + 4)
y - 6 = -¾x - 3
y - 6 + 6 = -¾x - 3 + 6
y = -¾x + 3 ⇒ also matches the given equation. Therefore, Option A is also correct.
Test Option B:
To find out whether Option B is also a correct answer, transform its equation into its slope-intercept form, y = mx + b:
3x + 4y = 12
3x - 3x + 4y = -3x + 12
4y = -3x + 12
Divide both sides by 4:
[tex]\frac{4y}{4} = \frac{-3x + 12}{4}[/tex]
y = -¾ + 3 ⇒ also matches the given equation. Therefore, Option B is also correct.
Thus, the correct answer is Option D) All of the above.
