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

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
$y = - 3x$

Answer 2

Answer:

The equation of the graph that is represented is:

                         $y=-3x$    

Step-by-step 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:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

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

$y-12=\dfrac{0-12}{0-(-4)}\times (x-(-4))\\\\i.e.\\\\y-12=\dfrac{-12}{0+4}\times (x+4)\\\\i.e.\\\\y-12=\dfrac{-12}{4}\times (x+4)\\\\i.e.\\\\y-12=-3(x+4)\\\\i.e.\\\\y-12=-3x-12\\\\i.e.\\\\y=-3x$

Hence, the equation of line is:

                   $y=-3x$