Answer
(A) $5x-2y=14$.
Work Step by Step
The standard slope intercept form is
$\Rightarrow y=mx+c$
Option (A):-$5x-2y=14$
$\Rightarrow y=\frac{5}{2}x-7$
$m=\frac{5}{2}$
For the $x-$intercept, substitute $y=0$.
$\Rightarrow 0=\frac{5}{2}x-7$
Solve for $x$.
$\Rightarrow \frac{14}{5}=x$
Hence, Option (A) is correct.
Option (B):-$-5x-2y=14$
$\Rightarrow y=-\frac{5}{2}x-7$
$m=-\frac{5}{2}$
For the $x-$intercept, substitute $y=0$.
$\Rightarrow 0=-\frac{5}{2}x-7$
Solve for $x$.
$\Rightarrow -\frac{14}{5}=x$
Hence, Option (B) is not correct.
Option (C):-$-5x+2y=14$
$\Rightarrow y=\frac{5}{2}x+7$
$m=\frac{5}{2}$
For the $x-$intercept, substitute $y=0$.
$\Rightarrow 0=\frac{5}{2}x+7$
Solve for $x$.
$\Rightarrow -\frac{14}{5}=x$
Hence, Option (C) is not correct.
Option (D):-$5x+2y=-14$
$\Rightarrow y=-\frac{5}{2}x-7$
$m=-\frac{5}{2}$
For the $x-$intercept, substitute $y=0$.
$\Rightarrow 0=-\frac{5}{2}x-7$
Solve for $x$.
$\Rightarrow -\frac{14}{5}=x$
Hence, Option (D) is not correct.
