Question

Which equation can be represented by the graph below (alegbra help)

Answer 1

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:

$\frac{4y}{4} = \frac{-3x + 12}{4}$

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.