The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
Step-by-step explanation:
The point-slope form of a linear equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where
∵ Point A = (10 , 15)
∵ The x-coordinate of the second point is 125% of x-coordinate
of point A
∴ x-coordinate of second point = [tex]\frac{125}{100}[/tex] × 10
∴ x-coordinate of second point = 12.5
∵ The y-coordinate of the second point is 75% of y-coordinate
of point A
∴ y-coordinate of second point = [tex]\frac{75}{100}[/tex] × 15
∴ y-coordinate of second point = 11.25
∴ The coordinates of the second point are (12.5 , 11.25)
Let us find the slope of the line by using the rule of it above
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
∵ [tex](x_{2},y_{2})[/tex] = (12.5 , 11.25)
∴ [tex]m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}[/tex]
Now we can write the equation
∵ The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex]
∵ [tex]m=-\frac{3}{2}[/tex]
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
- Substitute these values in the form of the equation
∴ y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
Learn more:
You can learn more about the linear equation in brainly.com/question/4152194
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