Question 84892
For the linear equation in standard form 2x + 5y = 6:
:
a) Find the slope of this line:
Find the slope by putting the equation into the slope/intercept form y = mx + b
2x + 5y = 6:
5y = -2x + 6; subtracted 2x from both sides
y = -(2/5)x + (6/5)
Slope (m) = -2/5
:
b) Find the slope of a line parallel to this line
Parallel lines have equal slopes, therefore its slope = -2/5 also
:
c) Find the slope of a line perpendicular to this line
The relationship of slopes of perpendicular lines: m1*m2 = -1
-2/5 * m2 = -1
m2 = -1 * -5/2
m2 = +5/2 is the slope of a perpendicular line
:
d) use your answers to part c) to write the equation of the line which is perpendicular to the given line and passes through the point (-3,-4).
Use the point/slope form y - y1 = m(x - x1)
x1 = -3; y1 = -4; m = 5/2
y - (-4) = 5/2(x - (-3))
y + 4 = 5/2 (x + 3)
y + 4 = (5/2)x + 15/2
y = (5/2)x + 15/2 - 4
Y = (5/2)x + 15/2 - 8/2
y = (5/2)x + 7/2
:
Put final equation in standard form:
Multiply equation  by 2 to get rid of the denominators
2y = 5x + 7; subtract 5x from both sides
-5x + 2y = 7;  the standard form