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Ron-Jon and Lena-Jon attempted to write the equation of the line that passes through the points $(2,1)$ and $(5,-5).$ To determine who is correct, we will find the equation and compare it with their answers. Let's write the equation in slope-intercept form.
$y=mx+b $
Here, $m$ is the slope and $b$ is the $y-$intercept. We will find the slope using the slope formula.
Now that we know that the slope of the line is $2,$ we can partially write its equation.
$y=-2x+b $
To find the $y-$intercept $b,$ we can substitute either given point into the above equation. Let's use $(2,1)$ and substitute $2$ for $x$ and $1$ for $y.$
We can now write the complete equation of the line.
$y=-2x−5 $
We obtained the same equation as Lena-Jon, and thus she is correct. Probably, Ron-Jon substituted the points in the wrong order when finding the slope.

$m=x_{2}−x_{1}y_{2}−y_{1} $

$m=5−2-5−1 $

SubTermsSubtract terms

$m=3-6 $

CalcQuotCalculate quotient

$m=-2$

$y=-2x+b$

$1=-2⋅2+b$

Solve for $b$

$b=5$