Question 1205639
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Let's find the slope.
{{{matrix(1,15,"Given","points:","(",x[1],",",y[1],") = ","(-4,-2)","and","(",x[2],",",y[2],") = ","(11,-14)")}}}


{{{m = slope = rise/run = matrix(1,3,"change","in","y")/matrix(1,3,"change","in","x")= (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (-14 - (-2))/(11 - (-4))}}}


{{{m = (-14 + 2)/(11 + 4)}}}


{{{m = (-12)/(15)}}}


{{{m = -4/5}}}
The slope is m = -4/5.
It will mean "go down 4, then right 5".


Now apply point-slope form.
{{{y - y[1] = m(x - x[1])}}}


{{{y - (-2) = -expr(4/5)(x - (-4))}}}


{{{y +2 = -expr(4/5)(x +4)}}}


{{{y +2 = -expr(4/5)x + (-4/5)*(4)}}}


{{{y +2 = -expr(4/5)x -16/5}}}


{{{y = -expr(4/5)x -16/5-2}}}


{{{y = -expr(4/5)x -16/5-10/5}}}


{{{y = -expr(4/5)x +(-16-10)/5}}}


{{{y = -expr(4/5)x -26/5}}}


{{{y = -0.8x - 5.2}}}
The result is in slope-intercept form (y = mx+b)
m = -4/5 = -0.8 = slope
b = -26/5 = -5.2 = y intercept


To verify, plug in x = -4 and you should get y = -2.
Also, plug in x = 11 and you should get y = -14.
I'll leave this verification scratch work for the student to do.
Desmos and GeoGebra are recommended graphing tools to visually verify the answer.
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