Question 1023050: Find an equation of the line that satisfies the given conditions. Your answers should be in slope-intercept form.
(a) x-intercept -8; y-intercept of 6
(b) through (1,1) and perpendicular to the line 4x-8y=1
(c) through (4,5) and parallel to the y-axis
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
(a) x-intercept -8; y-intercept of 6
Gradient = 6/-8 = -3/4
Using line equation y - b = m(x - a)
m = -3/4 and (a,b) = (-8, 0)
y - 0 = -3/4(x -(-8))
y = -3/4(x + 8)
y = -3/4x - 6
...............
(b) through (1,1) and perpendicular to the line 4x-8y=1
Sort 4x - 8y = 1 into y = mx + c form
-8y = -4x + 1
y = -4/-8 x + 1/-8
y = 1/2x - 1/8
Lines that are perpendicular to each other
have gradients that multiply together to
give -1
m1 x m2 = -1
1/2 x m2 = -1
m2 = -2
Using line equation y - b = m(x - a)
m = -2 and (a,b) = (1,1)
y - 1 = -2(x - 1)
y - 1 = -2x + 2
y = -2x + 2 + 1
y = -2x + 3
..............
(c) through (4,5) and parallel to the y-axis
A line parallel to the y axis would have 0 gradient.
Equation would be x = 4
Hope this helps :-)
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