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,

$m=\frac{y_2-y_1}{x_2-x_1}$

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

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

$m=\frac{-2-0}{0-3}$

$m=\frac{-2}{-3}$

$m=\frac{2}{3}$

Thus, the slope of the equation is $m=\frac{2}{3}$

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;

$y=\frac{2}{3}x-2$

Taking LCM, we have;

$y=\frac{2x-6}{3}$

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.