The equation of the line that passes through points (3 , -2) and (5 , -1)
is [tex]y+2=\frac{1}{2}(x-3)[/tex]
Step-by-step explanation:
The equation of a line in point slope form is:
[tex]y-y_{1}=m(x-x_{1})[/tex], where m is the lope of the line and [tex](x_{1},y_{1})[/tex]
are the coordinates of a point lies on the line
The slope of a line that contains points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Write the equation:
1. That passes through the points (3 , -2) and (5 , -1)
2. Put your answer in fully reduced point-slope form
Let point (3 , -2) = [tex](x_{1},y_{1})[/tex] and point (5 , -1) = [tex](x_{2},y_{2})[/tex]
∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ [tex]m=\frac{-1-(-2)}{5-3}=\frac{-1+2}{2}=\frac{1}{2}[/tex]
∵ The equation of the line is [tex]y-y_{1}=m(x-x_{1})[/tex]
∵ [tex](x_{1},y_{1})[/tex] = (3 , -2)
∵ m = [tex]\frac{1}{2}[/tex]
- Substitute the coordinates of the point and m in the equation
∴ [tex]y-(-2)=\frac{1}{2}(x-3)[/tex]
∴ [tex]y+2=\frac{1}{2}(x-3)[/tex]
The equation of the line that passes through points (3 , -2) and (5 , -1)
is [tex]y+2=\frac{1}{2}(x-3)[/tex]
Learn more:
You can learn more about equation the line in brainly.com/question/12967961
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