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Use the point-slope formula to write an equation of the line that passes through (- 1, 4) and (1, 5 ) .Write the answer in slope-intercept form (if possible).The equation of the line is Hi everyone, this is very hard for me I have tried 18 times by myself before I found you folks .I need this in the simplest terms as i don't get it if it is too involved .

User Laxmi Kadariya
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1 Answer

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To solve this problem, we will compute the slope of the line and then we will use it to find the equation of the line.

To determine the slope of a line that passes through points (x₁,y₁), and (x₂,y₂), we can use the following formula:


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

Substituting


\begin{gathered} (x_2,y_2)=(-1,4), \\ (x_1,y_1)=(1,5), \end{gathered}

in the above formula, we get:


s=(4-5)/(-1-1)=(-1)/(-2)=(1)/(2).

Now, with the above slope, we use the following formula for the equation of a line with slope m:


y-y_1=m(x-x_1).

Finally, we substitute one of the points:


y-5=(1)/(2)(x-1)

and take the equation to its slope-intercept form:


\begin{gathered} y-5=(1)/(2)(x-1), \\ y-5=(1)/(2)x-(1)/(2), \\ y=(1)/(2)x+(9)/(2). \end{gathered}

Answer:


y=(1)/(2)x+(9)/(2)=0.5x+4.5.

User Raymonad
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