#### Answer

$\text{a) Slope-Intercept Form: }
y=-9x+13
\\\\\text{b) Standard Form: }
9x+y=13$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the equation of the line that passes through the given points $(
2,-5
)$ and $(
1,4
),$ use the Two-Point Form of linear equations. Give the equation in the Slope-Intercept Form and in the Standard Form.
$\bf{\text{Solution Details:}}$
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, where
\begin{array}{l}\require{cancel}
x_1=2
,\\x_2=1
,\\y_1=-5
,\\y_2=4
,\end{array}
the equation of the line is
\begin{array}{l}\require{cancel}
y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)
\\\\
y-(-5)=\dfrac{-5-4}{2-1}(x-2)
\\\\
y+5=\dfrac{-9}{1}(x-2)
\\\\
y+5=-9(x-2)
.\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+5=-9(x-2)
\\\\
y+5=-9(x)-9(-2)
\\\\
y+5=-9x+18
\\\\
y=-9x+18-5
\\\\
y=-9x+13
.\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=-9x+13
\\\\
9x+y=13
.\end{array}
The equation of the line is
\begin{array}{l}\require{cancel}
\text{a) Slope-Intercept Form: }
y=-9x+13
\\\\\text{b) Standard Form: }
9x+y=13
.\end{array}