Question

Which equation does the graph below represent? (1 point)

A coordinate grid is shown. The x-axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y-axis values are from negative 15 to positive 15 in increments of 3 for each grid line. A line is shown passing through the ordered pairs negative 4, 12 and 0, 0 and 4, negative 12.

y = fraction negative 1 over 3x

y = −3x

y = 3x

y = fraction 1 over 3x

Answer 1

The equation of the graph that is represented is:

`y=-3x`

Explanation:

We know that the equation of a line passing through two points (a,b) and (c,d) is calculated by the using the two-point formula:

`y-b=(d-b)/(c-a)* (x-a)`

From the graph we observe that the line passes through (-4,12) and (0,0)

`y-12=(0-12)/(0-(-4))* (x-(-4))\\\\i.e.\\\\y-12=(-12)/(0+4)* (x+4)\\\\i.e.\\\\y-12=(-12)/(4)* (x+4)\\\\i.e.\\\\y-12=-3(x+4)\\\\i.e.\\\\y-12=-3x-12\\\\i.e.\\\\y=-3x`

Hence, the equation of line is:

`y=-3x`

Answer 2

ANSWER


`y = - 3x`



EXPLANATION


The graph passes through (0,0) and (-1,3).


The equation of a line passing through the origin is of the form,


`y = mx`

We now substitute (-1,3) to obtain,



`3 = - m`

This implies that,


`m = - 3`
The equation is

`y = - 3x`