The point-slope equation of the line is [tex]y-3=\frac{1}{5}(x-2)[/tex]
Step-by-step explanation:
The form of the point-slope equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where
- m is the lope of the line
- [tex](x_{1},y_{1})[/tex] is a point lies on the line
The slope of a line [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line
∵ The line through (2 , 3) and (7 , 4)
∴ [tex]x_{1}[/tex] = 2 and [tex]x_{2}[/tex] = 7
∴ [tex]y_{1}[/tex] = 3 and [tex]y_{2}[/tex] = 4
- Substitute these value in the rule of the slope
∵ [tex]m=\frac{4-3}{7-2}=\frac{1}{5}[/tex]
∴ the slope of the line is [tex]m=\frac{1}{5}[/tex]
Let us substitute the value of the slope and the coordinates of point [tex](x_{1},y_{1})[/tex] in the form of the equation
∵ [tex]y-y_{1}=m(x-x_{1})[/tex]
∵ [tex]x_{1}[/tex] = 2 and [tex]y_{1}[/tex] = 3
∵ [tex]m=\frac{1}{5}[/tex]
∴ [tex]y-3=\frac{1}{5}(x-2)[/tex]
The point-slope equation of the line is [tex]y-3=\frac{1}{5}(x-2)[/tex]
Learn more:
You can learn more about the linear equation in brainly.com/question/12941985
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