Answer:
The equation of the line in point-slope form is [tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex].
Step-by-step explanation:
According to the statement, let [tex]A(x,y) = (14,21)[/tex] and [tex]B(x,y) = (1.25\cdot x_{A},0.75\cdot y_{A})[/tex]. The equation of the line in point-slope form is defined by the following formula:
[tex]y-y_{A} = m\cdot (x-x_{A})[/tex] (1)
Where:
[tex]x_{A}[/tex], [tex]y_{A}[/tex] - Coordinates of the point A, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
In addition, the slope of the line is defined by:
[tex]m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (2)
If we know that [tex]x_{A} = 14[/tex] and [tex]y_{A} = 21[/tex], then the equation of the line in point-slope form is:
[tex]x_{B} = 1.25\cdot (14)[/tex]
[tex]x_{B} = 17.5[/tex]
[tex]y_{B} = 0.75\cdot (21)[/tex]
[tex]y_{B} = 15.75[/tex]
From (2):
[tex]m = \frac{15.75-21}{17.5-14}[/tex]
[tex]m = -\frac{3}{2}[/tex]
By (1):
[tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex]
The equation of the line in point-slope form is [tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex].
