Answer
$(a)$ Slope measures steepness of a line. The slope of a line is change in $y$ divided by change in $x$ of $2$ points on a line. Let $m$ be slope.
$m=-3$
$(b)$ In general, a linear equation has a form: $y=mx+b$, where $b$ is $y$-intercept and $m$ is a slope.
So, we will give the equation a general form and get: $y=-2x+4$
$m=-2$ and $b=4$
$(c)$ Using the point-slope form of the linear equation, that is $y_2-y_1=m(x_2-x_1)$ we can write:
$y=3x-1$
Work Step by Step
$(a)$ Slope measures steepness of a line. The slope of a line is change in $y$ divided by change in $x$ of $2$ points on a line. Let $m$ be slope.
$m=\frac{-2-4}{1-(-1)}=\frac{-6}{2}=-3$
$(b)$ First we have to write $y$ in terms of $x$
$3y=-6x+12$
$y=-2x+4$
In general, a linear equation has a form: $y=mx+b$, where $b$ is $y$-intercept and $m$ is a slope.
We have $m=-2$ and $b=4$
$(c)$ Using the point-slope form of the linear equation, that is $y_2-y_1=m(x_2-x_1)$ we can write:
$y-2=3x-1$
$y=3x-1$
