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frutty [35]
3 years ago
8

A line passes through point A (14,21). A second point on the line has an x-value that is 125% of the x-value of point A and a y-

value
that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.

?:(
Mathematics
1 answer:
seropon [69]3 years ago
5 0

Answer:

The equation of the line in point-slope form is y-21 = - \frac{3}{2}\cdot (x-14).

Step-by-step explanation:

According to the statement, let A(x,y) = (14,21) and B(x,y) = (1.25\cdot x_{A},0.75\cdot y_{A}). The equation of the line in point-slope form is defined by the following formula:

y-y_{A} = m\cdot (x-x_{A}) (1)

Where:

x_{A}, y_{A} - Coordinates of the point A, dimensionless.

m - Slope, dimensionless.

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

In addition, the slope of the line is defined by:

m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}} (2)

If we know that x_{A} = 14 and y_{A} = 21, then the equation of the line in point-slope form is:

x_{B} = 1.25\cdot (14)

x_{B} = 17.5

y_{B} = 0.75\cdot (21)

y_{B} = 15.75

From (2):

m = \frac{15.75-21}{17.5-14}

m = -\frac{3}{2}

By (1):

y-21 = - \frac{3}{2}\cdot (x-14)

The equation of the line in point-slope form is y-21 = - \frac{3}{2}\cdot (x-14).

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