Question

Identify the equation that goes with the graph below using the x and y intercepts.

a. y + 2x = 8
b. 4y - 2x = -8
c. 1/2y + 2x = -8
d. 2y + 4x = -8

Answer 1

The identification of the equation that goes with the graph using the x and y intercepts is b. 4y - 2x = -8.

To find the equation of the line using the x and y intercepts, use the formula:

`( (x)/(a) + (y)/(b) = 1 )`

Where:

The x-intercept = a

The y-intercept = b

Given the coordinates (4, 0) and (0, -2), the x-intercept and y-intercept are:

The x-intercept is (4, 0), so (a = 4), and the y-intercept is (0, -2), so (b = -2).

Substituting these values into the formula:

`( (x)/(4) + (y)/(-2) = 1 )`

Multiplying through by 4 to clear the fraction:

(x - 2y = 4)

Therefore, the equation of the line is (x - 2y = 4), which is equivalent to 4y - 2x = -8 when rearranged as follows:

We can rearrange (x - 2y = 4) to get (-2y = -x + 4), and then multiply every term by -2 to get (4y - 2x = -8).

Thus, the correct equation is Option B.