Question

Use function notation to write the equation of the line. please help

Answer 1

Therefore the equation of the line in function-form is f(x)=-2x-1

An equation of a line on the cartesian plane is given by y=mx+c. Here m denotes the slope of the line and c denotes the y-intercept.

Slope of a line is defined as the inclination of the line along the positive   x- axis . Slope is calculated by the formula $m=\frac{y_2-y_1}{x_2-x_1}.$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

y-intercept is defined as the point where the line passes through the y-axis.

From the graph we can see that the line passes through (0,-1)and (-1,1)

therefore slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}\\or, m=\frac{1-(-1)}{-1-0}\\or, m=-2$

Now we know that the equation of a line passing through a point $(x_1,y_1)$ and with slope m is given by

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

Substituting the values in the equation we get

y-(-1)=-2(x-0)

or, y=-1-2x

Therefore the equation of the line in function-form is f(x)=-2x-1 .Hence the second option is correct.

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