Having trouble finding and writing equations?

Question

Question 1:

Find an equation of the line containing the given pair of points. Write your answer in slope-intercept form.

(1, -5) and (5, 3)


Question 2:
Write an equation of the line described.
Through (-2, 7), perpendicular to 2x + 7y = -53



With question two with trying to find the slope I end up with;
y=-2x/7 - 53/7 and thats where I get confused

Any help would be greatly appreciated. Thanks.

Answer 1

Question 1
m = (3 + 5) / (5 - 1) = 8 / 4 = 2
y - 3 = 2 (x - 5)
y = 2x - 10 + 3
y = 2x - 7

Question 2
2x + 7y = - 53
7y = - 2x - 53
y = ( - 2 / 7 ) x - 53 / 7
m = (7 / 2) is gradient of required line.
y - 7 = (7 / 2) ( x + 2 )
y - 7 = ( 7 / 2 ) x + 7
y = ( 7 / 2 ) x + 14

Answer 2

1) find the slope between the two points given with the slope formula.
(y2 - y1) / (x2 - x1)

this gives: (3-1)/(5-(-5)) = 2/10 = 1/5. so m = 1/5.

with a slope and either point, you then use the point-slope formula.
y - y1 = m(x - x1) [think of it as a rewritten form of the slope formula]

then we get y - 3 = 1/5 (x - 5)
=> y - 3 = 1/5 x - 1
=> y = 1/5x + 2

2) perpendicular means the negative reciprical of the original slope.
so: 7y = -2x -53
=> y = -2/7x - 53/7
original slope = -2/7, so perpendicular slope = 7/2

m= 7/2 P(-2,7)

Use point slope formula again

=> y - 7 = 7/2(x+2)
=> y - 7 = 7/2x + 7
=> y = 7/2x + 14

hope that helps. gtgkkbye

Answer 3

Hi,

Question 1:

Find an equation of the line containing the given pair of points. Write your answer in slope-intercept form.

(1, -5) and (5, 3)

m = (-5 - 3)/(1 - 5) = -8/-4 = 2

The equation in point-slope form is y - y1 = m(x - x1) which is:

y - 3 = 2(x - 5)
y - 3 = 2x - 10
y = 2x - 7 <== answer



Question 2:
Write an equation of the line described.
Through (-2, 7), perpendicular to 2x + 7y = -53

First, find the slope of 2x + 7y = -53 by solving it for y.

2x + 7y = -53
7y = -2x - 53
y = -2/7x - 53/7

The slope of this line is -2/7, so a perpendicular slope is its negative reciprocal, 7/2. (For the perpendicular slope, you have to flip your slope upside down AND change its sign.)

The equation in point-slope form is y - y1 = m(x - x1) which is:

y - 7 = 7/2(x + 2)
y - 7 = 7/2x + 7
y = 7/2x + 14 <== answer


With question two with trying to find the slope I end up with;
y=-2x/7 - 53/7 and thats where I get confused
You did not use 7/2 as your perpendicular slope!!

I hope that helps!! :-)

Answer 4

the first question we must first find the slope... so (y1 - y2)/(x1 - x2)

(3 - -5)/(5 - 1) or 8/4 which is 2

we then write it as y - y1 = m(x - x1) (m is the slope)
so it is y - 3 = 2(x - 5)
then it becomes y - 3 = 2x - 10 next add the 3 to both sides
y = 2x - 7


with question 2 we must again find the slope first
2x+ 7y = -53 subtract 2x from both sides
7y = -2x - 53 divide both sides by 7
y = -2/7 x - 53/7 the slope will be -2/7... to find perpendicular, we need the opposite reciprocal of - 2/7 which is 7/2, plug this in with the point already given and we'll get

y - 7 = 7/2(x + 2)
y - 7 = 7/2x + 7 add 7 to both sides
y = 7/2x + 14

Answer 5

The slope-intercept form of a straight line is
y=mx+b. mis the slope ,b is the y-intercept.
m=rise/run =y(2)-y(1) / x(2)-x(1)
m=3-(-5)/5-1, =8/4, =2
Our equation now begins to take shape. y=2x+b
Now to find a value for b
(5,3) lies on the line, {So does (1,-5) but I picked (5,3) because I hate - signs}
Substitute 5 for x, 3 for y, to find b
y=2x+b
3=2(5)+b
3=10+b
-7=b
Our equation is y =2x-7

Lines that are perpendicular have slopes that are negative reciprocals of each other. If Line 1 has a slope of 3, Line 2, if perpendicular, would have a slope of -1/3
With that background , let's proceed.
We want the equation of a line
A) through(-2,7)
b) perpendicular to 2x+7y=-53
I see you converted 2x+7y=-53 to y=-(2/7)x-53/7.
Good! We need that. From your work, we see this line has a slope of -2/7. We want a line perpendicular to this line, so the required line will have a slope of 7/2. Our desired equation is y=7/2 x+b
To get b, substitute -2 for x, and 7 for y.
y=7/2x+b
7=7/2(-2)+b
7=-7+b
b=14
Our desired equation is y=(7/2)x+14. If you wish you can write this as 2y=7x+28.
That's it!

Answer 6

Question 1:
You need to put it in slope-intercept form. There's a formula for this. To find the slope; it's:
(y2 - y1)/(x2 - x1) = m

The x and y represent the values of the coordinates. Plug them in:

(1, -5) and (5, 3)
(y2 - y1)/(x2 - x1) = m
(3 - (-5))/(5 - 1)
8 / 4
m = 2

Then you use the slope-intercept equation to find the rest. It's
y = mx + b

You already know the m (you just found it, it's 2)...so use one of the coordinates for the rest to find b. I suggest using the (5, 3) since it's easier.

y = mx + b
3 = 2(5) + b
3 = 10 + b
b = -7

So just rewrite the equation *without* the x and y:

y = 2x - 7

You should get the same thing if you used the other coordinates also:

y = mx + b
-5 = 2(1) + b
-5 = 2 + b
-7 = b

Same equation... y = 2x - 7

If you had to put it in the other format, it would be:

-2x + y = -7

Answer 7

question 1
y=(3-(-5))/(5-1)x + b
y=8/4x +b
y=2x+b
-5=2(1)+b
b=-7
y=2x-7

Question 2
You are right as far as you go. y = -2x/7-53/7 means the slope is -2/7. For a line perpendicular you need a slope that is the negative reciprocal or 7/2
y=7x/2 + b
7=7(-2)/2+b
b=14
y=7x/2+14

Answer 8

haha pre calc or algebra huh.. well first of all you find the slope 8/4(2) so then you take one point and put it into (Y-Y1)=M(X-X1) you put the slope in for M and pick one point i would pick (5,3) there are no negatives so then you have (Y-3)=2(X-5) Y-3=2X-10 so Y=2X-7ok
2.ok you have to write this equation in slope intercept for solve for Y Y=7/2X-53/7 (negative recipricol for perpendicular lines) now you do that (Y-Y1)=M(X-X1) and get Y=7/2X+14

Answer 9

"for the perpendicular slope, I'll flip this slope and change the sign."

m = (y1 - y2) / (x1 -x2) [= rise / run]

for x = 0; y= -53/7 point (0 ; -53/7)

for y = 0; x = -53/2 point (-53/2 ; 0)

m = (-53/7 -0) / (0 - -53/2) = -2/7


the rest you get on the link, ok?