Answer to Question #134439 in Analytic Geometry for Kimberly

Question

Determine the equation of the line that passes thru P1(4,-8) and P2(0, ¾).

Answer 1

The equation of a line that passes trough (x1,y1) and (x2,y2) is

$\displaystyle \frac{x-x_1}{x_2-x_1} = \frac{y-y_1}{y_2-y_1}$

Equation of the line that passes trough P1(4,-8) and P2(0, 0.75) is

$\displaystyle \frac{x-4}{0-4} = \frac{y-(-8)}{0.75-(-8)}$

$\displaystyle \frac{x-4}{-4} = \frac{y+8}{8.75}$

$8.75 (x-4) = -4 (y+8)$

$8.75 x- 35 = -4 y -32$

$8.75x + 4y -3=0$ or

$\displaystyle y =\frac{ -8.75x+3}{4} = -2 \frac{3}{16}x + \frac{3}{4} = -2.1875x+0.75$

Answer: $y=-2.1875x+0.75$