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Find an equation for the line that passes through the points (-5,-1) and (5,4)

User Acrollet
by
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1 Answer

5 votes

Answer:

y = 0.5x + 1.5

Step-by-step explanation:

The equation of a line that passes through two points (x₁, y₁) and (x₂, y₂) can be calculated as:


y-y_1=m(x-x_1)

Where m is the slope and it is equal to:


m=(y_2-y_1)/(x_2-x_1)

So, if we replace (x₁, y₁) by (-5, -1) and (x₂, y₂) by (5, 4), we get that the slope is equal to:


m=(4-(-1))/(5-(-5))=(4+1)/(5+5)=(5)/(10)=0.5

Then, the equation of the line is:


\begin{gathered} y-(-1)=0.5(x-(-5)) \\ y+1=0.5(x+5) \end{gathered}

Finally, if we solve for y, we get:


\begin{gathered} y+1=0.5x+0.5(5) \\ y+1=0.5x+2.5 \\ y+1-1=0.5x+2.5-1 \\ y=0.5x+1.5 \end{gathered}

So, the equation of the line is:

y = 0.5x + 1.5

User Alexmcfarlane
by
8.2k points

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