Question

Which of the following is a correct equation for the linear graph shown below?

(1) 2y+3x=-6
(2) 3y-2x=-6
(3) 2y+3x-2
(4) 3y-2x=-2

Answer 1

Given:

Given that the graph of the line.

We need to determine the equation of the line.

Slope:

The slope of the line can be determined using the formula,

`m=(y_2-y_1)/(x_2-x_1)`

Let us substitute any two points that the line passes through.

Substituting the point (3,0) and (0,-2) in the formula, we get;

`m=(-2-0)/(0-3)`

`m=(-2)/(-3)`

`m=(2)/(3)`

Thus, the slope of the equation is
`m=(2)/(3)`

y - intercept:

The y - intercept of the equation is the point at which the line passes through the y - axis.

Thus, from the graph, the value of y - intercept is b = -2.

Equation of the line:

The equation of the line can be determined using the formula,

`y = mx+b`

Substituting the values, we have;

`y=(2)/(3)x-2`

Taking LCM, we have;

`y=(2x-6)/(3)`

Multiplying both sides by 3, we get;

`3y=2x-6`

Subtracting both sides by 2x, we get;

`3y-2x=-6`

Thus, the equation of the line is
`3y-2x=-6`

Hence, Option 2 is the correct answer.