Question

Wich of the following represents the equation of the graph below ?

Answer 1

To find the equation, use the slope intercept form:

y = mx + b

where m is the slope and b is the y-intercept

Take the points on the graph:

(x1, y1) ==> (3, -4)

(x2, y2) ==> (0, -2)

Find the slope using the formula below:

`m\text{ = }\frac{y2-y1}{x2\text{ - x1}}`
`m\text{ = }(-2-(-4))/(0-3)=(-2+4)/(0-3)=(2)/(-3)\text{ = -}(2)/(3)`

The y-intercept is the point where the line crosses the y-axis.

The y-intercept here is -2.

Therefore, we have the equation:

`y\text{ = -}(2)/(3)x\text{ - 2}`

Now, equate the equation above to zero:

`-y-(2)/(3)x-2\text{ = 0}`

Multiply through by -3, to eliminate the fraction:

`\begin{gathered} -y(-3)\text{ -}(2)/(3)x(-3)\text{ -2(-3) = 0} \\ \\ 3y\text{ + 2x + 6 = 0} \end{gathered}`

Therefore, the equation that represents the graph is:

3y + 2x + 6 = 0

ANSWER:

A) 3y + 2x + 6 = 0