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Write a linear equation that passes through the points (3, 1) and (-2, 6). ELE BE CE EL PR ET EM BRE SHO This

User Bastronaut
by
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1 Answer

23 votes
23 votes

Answer:

The equation of the line in slope intercept form is;


y=-x+4

And the equation of the line in point-slope form is;


y-1_{}=-1(x-3_{})

Step-by-step explanation:

We want to write a linear equation that passes through the points;


(3,1)\text{ and }(-2,6)

Firstly, let us find the slope of the line;


\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(6-1)/(-2-3) \\ m=(5)/(-5) \\ m=-1 \end{gathered}

So, we can now use the point-slope equation of line to find the equation of the line;


y-y_1=m(x-x_1)_{}

using the point given;


(x_1,y_1)=(3,1)

And the derived slope, we have;


\begin{gathered} y-y_1=m(x-x_1)_{} \\ y-1_{}=-1(x-3_{}) \\ y-1=-x+3 \\ y=-x+3+1 \\ y=-x+4 \end{gathered}

Therefore, the equation of the line in slope intercept form is;


y=-x+4

And the equation of the line in point-slope form is;


y-1_{}=-1(x-3_{})

User Jason Iverson
by
2.8k points
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