Write the equation of the line that passes through point (0, 7) with a slope of –5.?

Question

Determine which two equations represent perpendicular lines. (a) y = 3x – 7 (b) y =1/3 x + 7 ) (c) y = – 1/3x + 7 (d) y =1/3x – 7

Write the equation of the line passing through (–3, –5) and (3, 0).

Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1.

What is the ordered pairs solution for the equation 3x – 4y = 12?

Answer 1

I see a few people have given you the answers, here's how you can find them for yourself....
y = -5x + 7 You put the -5, the slope in front of the x, and make the y intercept, 7, stand alone in the form y = mx + b.

Compare the slopes. Perpendicular lines have slopes which are negative reciprocals, that is, the number you get if you flip it over and change the sign. The product of two negative reciprocals is -1. The slope is the number in front of the x. The only pair of numbers here which qualify as negative reciprocals is 3 and (-1/3) The equations that have these slopes which are negative reciprocals are a and c

Since one of these points is an x intercept, it's easy to use the point slope formula. First find the slope, m = (y2-y1)/(x2-x1) =
(0-(-5))/(3-(-3)) = 5/6
Next use this in the point slope form of the line
m(x-x1) = (y - y1). Let's use the easier point, (3,0)
(5/6)(x-3) = y which you can simplify to point slope form, or rewrite in standard form, if you wish, or if your directions say to do so.

This one's easy, once you understand about the information contained in the linear equation y = mx + b. You want a line perpendicular to a line with a slope of -3 (the number in front of the x of the given equation) so it needs a slope of 1/3. And the b has to be 5. So your equation is y = (1/3)x + 5

Assign a convenient value for x, plug it in, and find the corresponding y. There are infinitely many solutions. For example, if x = 4, y = 0. If x = 0, y = -3. Connect these points on the graph and extend the line. Any point on that line will be a solution to that equation.

These aren't hard onece you understand them. For tutorials on any subject put subject tutorial in your search window. For example I'll put linear equations tutorial in the search window and see what comes up...

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut21_graph.htm
http://www.nipissingu.ca/calculus/tutorials/linear.html
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut21_graph.htm

Answer 2

The Eq. of the line with slope -5 is y = -5x+c.
As it passes through (0,7), then 7=c. So the required Eq. is y= -5 x +7. Answer
Lines represented in (a) and (c) are perpendicular because the product of their slopes is - 1. Answer.
Eq. of the line passing through (-3,-5) is:
y+5=m(x+3). As it also passes through (3,0), we have
5=6m or m=5/6. So the desired Eq. is : y+5 =(5/6)(x+3).
Verify this answer. It is OK.
The slope of the line y = –3x + 1 is -3. The slope of the line perpendicular to it should be 1/3, so that their product is -1.So the Eq. of the line perpendicular to
y = –3x + 1 is y=(1/3)x+c. As the intercept on the y-axis is 5, c=5. So the desired Eq. is y=(1/3)x +5. Easily verified.
Putting y=0,3, 6, etc in 3x – 4y = 12, we get respectively x= 4, 8, 12, etc.
So some of the ordered pairs of solutions of this Eq. are
(4,0);(8,3);(12,6) etc.

Answer 3

1) The equation for a line that passes through (0,7) and has a slope of -5 is y=-5x+7

2) a and c are perpendicular (y=3x-7 and y=-1/3x+7)

3) The equation of the line passing through (-3,-5) and (3,0) is y=5/6x-5/2

4) The equation with the y-intercept at (0,5) and is perpendicular to y=-3x+1 is y=1/3x+5

5) The solution is at the x-intercept, and in this case, x=4, and the ordered pair is (0,4)

Answer 4

Y=-4/5x+7

Answer 5

perp lines slope are neg reciprocals
like of slope 3 is perp to line of slope -1/3
so a and c are perp

first find slope
change in y /change in x
-5-0/-3-3=-5/-6=5/6
use either point and point slope formula (y-y1)=m(x-x1)
y-0=5/6(x-3)
y = (5/6)x - 5/2

perp to linewith slope of -3 has slope of 1/3
again use point slope
y-5=1/3(x-0)
y - 5 = 1/3x
y = 1/3 x + 5

there are an infinite # of solutiond easiest to find are the intercepts
3(0) -4y =12
-4y = 12
y = -3
(0,-3)

or 3x -4y = 12
3x -4(0) = 12
3x =12
x = 4
(4,0)

or sub any # infor x and solve for y

Answer 6

pt-slope form: (y-y0)=m(x-x0)
Slope-intercept form: y=mx+b
1) (y-7)= -5(x-0)
y= -5x+7
2) Perpendicular lines have negatice recipricals for slopes, so a&c
3) slope = rise/run=5/6
y-0=(5/6)(x-3)
y=(5x/6)-(5/2)
4) slope is negative reciprocal, so 1/3
(y-5)=1/3(x-0)
y=x/3+5
5) unsolvable for two variables, but y=3/4x-3

Answer 7

1)Point-slope formula:
(y-y1)=m(x-x1)
y-7=-5x
y=-5x+7

2)a and c represent perpendicular lines:

3)Slope:
m=(y2-y1)/(x2-x1)
m=(0+5)/(3+3)
m=5/6

y+5=5/6(x+3)
y+5=5/6x+5/2
y=5/6x+5/2-10/2
y=5/6x-5/2

4)y-5=1/3x
y=1/3x+5

5)The solution set would be (8,3)
3(8)-4(3)=12
24-12=12
12=12