Answer
$\text{a) Slope-Intercept Form: }
y=3x+7
\\\\\text{b) Standard Form: }
3x-y=-7$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the equation of the line with the following properties:
\begin{array}{l}\require{cancel}
\text{Slope: }
3
\\\text{Through: }
(-1,4)
,\end{array}
use the Point-Slope Form of linear equations. Give the equation in the Slope-Intercept Form and in the Standard Form.
$\bf{\text{Solution Details:}}$
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions,
\begin{array}{l}\require{cancel}
y_1=4
,\\x_1=-1
,\\m=3
,\end{array}
is
\begin{array}{l}\require{cancel}
y-y_1=m(x-x_1)
\\\\
y-4=3(x-(-1))
\\\\
y-4=3(x+1)
.\end{array}
Using the properties of equality, in the form $y=mx+b$ or the Slope-Intercept Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-4=3(x+1)
\\\\
y-4=3(x)+3(1)
\\\\
y-4=3x+3
\\\\
y=3x+3+4
\\\\
y=3x+7
.\end{array}
Using the properties of equality, in the form $ax+by=c$ or the Standard Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=3x+7
\\\\
-3x+y=7
\\\\
-1(-3x+y)=-1(7)
\\\\
3x-y=-7
.\end{array}
The equation of the line is
\begin{array}{l}\require{cancel}
\text{a) Slope-Intercept Form: }
y=3x+7
\\\\\text{b) Standard Form: }
3x-y=-7
.\end{array}
