MATH SOLVE

4 months ago

Q:
# A line passes through point A(12,18)A(12,18). A second point on the line has an x-value that is 125% of the x-value of point AA and a y-value that is 75% of the y-value of point AA. Use point AA to write an equation of the line in point-slope form. An equation is y− __ =__ x(x−__).

Accepted Solution

A:

Let's find the coordinates of the second point.

x-coordinate: 1.25*12 = 15

y-coordinate: 0,75*18 = 13.5

The points are (12,18) and (15,13.5). Next, let's determine the slope, m.

m = Δy/Δx = (13.5 - 18)/(15 - 12) = -1.5

Then, we use the form of the point-slope formula: y = mx + b. Find b using point (12,18)

18 = (-1.5)(12) + b

Solving for b,

b = 36

Therefore, the equation is: y = -1.5x +36

x-coordinate: 1.25*12 = 15

y-coordinate: 0,75*18 = 13.5

The points are (12,18) and (15,13.5). Next, let's determine the slope, m.

m = Δy/Δx = (13.5 - 18)/(15 - 12) = -1.5

Then, we use the form of the point-slope formula: y = mx + b. Find b using point (12,18)

18 = (-1.5)(12) + b

Solving for b,

b = 36

Therefore, the equation is: y = -1.5x +36