Question

Complete the point-slope equation of the line through (2,3 and (7,4). Use exact numbers.

Answer 1

The point-slope equation of the line is $y-3=\frac{1}{5}(x-2)$

Step-by-step explanation:

The form of the point-slope equation is $y-y_{1}=m(x-x_{1})$ , where

• m is the lope of the line
• $(x_{1},y_{1})$ is a point lies on the line

The slope of a line $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points on the line

∵ The line through (2 , 3) and (7 , 4)

∴ $x_{1}$ = 2 and $x_{2}$ = 7

∴ $y_{1}$ = 3 and $y_{2}$ = 4

- Substitute these value in the rule of the slope

∵ $m=\frac{4-3}{7-2}=\frac{1}{5}$

∴ the slope of the line is $m=\frac{1}{5}$

Let us substitute the value of the slope and the coordinates of point $(x_{1},y_{1})$ in the form of the equation

∵ $y-y_{1}=m(x-x_{1})$

∵ $x_{1}$ = 2 and $y_{1}$ = 3

∵ $m=\frac{1}{5}$

∴ $y-3=\frac{1}{5}(x-2)$

The point-slope equation of the line is $y-3=\frac{1}{5}(x-2)$

Learn more:

You can learn more about the linear equation in brainly.com/question/12941985

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