Question

Which equation represents the line shown on the coordinate plane below??

Answer 1

The y-intercept=0 and the slope=-1/4,
so y=-1/4x represents the line.

Answer 2

A straight line is represented by a linear function.

The equation of the line is $y = -\frac 14 x$

From the coordinate plane, the line passes through the following points

$(x,y) =(0,0)\ (4,-1)$

The slope of the above points is calculated using:

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

So, the above equation becomes

$m = \frac{-1 - 0}{4-0}$

This gives

$m = \frac{-1}{4}$

Rewrite as:

$m = -\frac{1}{4}$

The line equation is then calculated as:

$y = m(x-x_1) + y_1$

So, we have:

$y = -\frac 14 (x-0) + 0$

This gives

$y = -\frac 14 (x)$

Remove bracket

$y = -\frac 14 x$

Hence, the equation of the line is $y = -\frac 14 x$

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