Which equation can be represented by the graph shown below?

The correct option is: Option: J

                               3x+8y-16=0

We are given a straight line that passes through the points (0,2).

Also we could observe that the line is a decreasing function since the line has a negative slope and positive y-intercept hence we will check from each of the given equation which has a negative slope.

F)

                     -3x+8y+16=0

on converting this equation to the slope-intercept form.

We observe that the equation takes the form:

            y=3/8 x-2

Here slope is: 3/8

and y-intercept is: -2

Hence, option: F is incorrect.

(Since slope is positive and y-intercept is negative)

G)

                         3x-8y+16=0

on converting this equation to the slope-intercept form.

We observe that the equation takes the form:

            y=3/8 x+2

Here slope is: 3/8

and y-intercept is: 2

Hence, option: G is incorrect.

(Since slope is positive )

H)

                    -3x-8y-16=0

on converting this equation to the slope-intercept form.

We observe that the equation takes the form:

            y= -3/8 x-2

Here slope is: -3/8

and y-intercept is: -2

Hence, option: G is incorrect.

(Since y-intercept is negative )

J)

                        3x+8y-16=0

on converting this equation to the slope-intercept form.

We observe that the equation takes the form:

                     y= -3/8 x+2

Here slope is: -3/8

and y-intercept is: 2

Hence, it satisfies the property of the line.

                          Hence, option: J is correct.

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