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

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] , wherem is the lope of the line[tex](x_{1},y_{1})[/tex] is a point lies on the lineThe 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#LearnwithBrainly