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We can write the equation for the line that connects the points in point-slope form.
$y−y_{1}=m(x−x_{1}) $
Here, where $m$ represents the slope and $(x_{1},y_{1})$ is a point on the line. To write the equation, we'll first need to determine the slope. To do this, we will use the slope formula and our two points.
The slope of the line is $-53 .$ We can now substitute the value for $m$ in the formula.
$y−y_{1}=-53 (x−x_{1}) $
We should now write **two** equations of the line. Thus, we will use both our points, $(1,-2)$ and $(-4,1),$ and substitute them for $x_{1}$ and $y_{1}$ to form two equations.
$y−(-2)=-53 (x−1)⇔y+2=-53 (x−1)y−1=-53 (x−(-4))⇔y−1=-53 (x+4) $
Any point that lies on the line can be used to write an equation in point-slope form. Our answer will be
$y+2=-53 (x−1)andy−1=-53 (x+4).$

$m=x_{2}−x_{1}y_{2}−y_{1} $

$m=-4−11−(-2) $

SubNeg$a−(-b)=a+b$

$m=-4−11+2 $

AddSubTermsAdd and subtract terms

$m=-53 $

MoveNegDenomToFracPut minus sign in front of fraction

$m=-53 $