Let line t be the line represented by x - 2y = 7and let line p be the line perpendicular to line t and containing the point (4,-4). What is the x-coordinate of the point common to line t and line p? Express your answer as a common fraction.
+128475 x - 2y =7 → 2y = x - 7 → y = (1/2)x - 7/2 the slope of t = (1/2)
The slope of a line perpendicuar to this = -2
And it contains the point ( 4, -4)
Equation of p
y = -2(x - 4) -4
y = -2x + 8 - 4
y = -2x + 4
x intersectionof these lines
(1/2) x - 7/2 = -2x + 4
2x + (1/2) x = 4 + 7/2
(4/2)x + ( 1/2) x = 8/2 + 7/2
(5/2) x = 15/2
x = (15/2) ( 2/5) = 30/10 = 3
See the graph, here : https://www.desmos.com/calculator/s0denwkyj8
