Algebra Problems, HELP?
1) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx + b
(4,5); x + 7y = 4
The equation of the line is y = ?
2) Find an equation of the line having the given slope and containing the given point.
m = 5/6, (3, -5)
3) find an equation of the line containing the given pair of points.
(-1,-6) and (-4, -7)
The equation of the line is y = ?
4) Find an equation of the line containing the given pair of points.
[ 1/4, - 1/2] and [ 3/4, 4]
What is the equation of the line?
y=
(simplify all answers)
Please explain how you got the answer in each question (step by step). I really appreciate any help you give.
Comments
all these can be done with the following formulas:
y - y1 = m(x - x1) and m = (y2 - y1) / (x2 - x1)
y - 5 = (-1 / 7)(x - 4)
y - 5 = ( - 1 / 7)x + 4 / 7
y = ( -1 / 7)x + (39 / 7)
1) (4,5); x + 7y = 4
Put the equation in point-slope form (solve for y)
x + 7y = 4
7y = -x + 4
y = -1/7 * x + 4/7
The slope of the line is -1/7, so the slope of the parallel line is -1/7. Plug in -1/7 for m and (4,5) for x and y to find b.
y = mx + b
5 = -1/7 * 4 + b
5 = -4/7 + b
b = 5 + 4/7
b = 39/7
The equation of the line is y = -1/7 * x - 39/7
2) Same as the second part of #1. Plug the numbers into y = mx + b.
6 = 5/6 * 3 + b
6 = 15/6 + b
b = 6 - 15/6
b = 21/6
b = 7/2
y = 5/6 * x + 7/2
3) (-1,-6) and (-4, -7). First find the slope.
m = (y2 - y1) / (x2 - x1)
m = (-7 - (-6)) / (-4 - (-1))
m = -1 / -3
m = 1/3
Plug in m and one of the points to find b.
y = mx + b
-6 = 1/3 * (-1) + b
b = -6 + 1/3
b = -17/3
The equation of the line is y = 1/3 * x - 17/3
4) (1/4, -1/2) and (3/4, 4). Same thing. Find the slope first.
m = (4 - (-1/2)) / (3/4 - 1/4)
m = 7/2 / 1/2
m = 7
Find b
-1/2 = 7 * 1/4 + b
b = -1/2 - 7/4
b = -9/4
What is the equation of the line? y = 7x - 9/4
I hope I explained it clearly enough.