Question

Find the value of y so that the line passing through (6, y) and (7, 5) has a slope of -3.

Answer 1

Using the gradient formula
\[M = \frac{y2-y1}{x2-x1}\]
we have m/gradient which is -3
and two points (6,y) and (7,5)
x1,y1 x2,y2
substitute the gradient x1,y1,x2 and y2 into the formula and solve.

Answer 2

or just use graph paper. you want the point with x=6 to go down three units over to the point (7,5).

Answer 3

yeh, that is if graph paper is available to you and it's better to use a calculation method like the one I used.

Answer 4

more accurate and efficient.

Answer 5

but how do you substitute for the gradient form, if you only have one coordinate with both y & x?

Answer 6

k, let me show you.

Answer 7

Using m=-3 and (6,y) (7,5)
x1,y1 x2,y2
\[M = \frac{y2-y1}{x2-x1}\]
\[-3=\frac{5-y1}{7-6}\]
\[-3=\frac{5-y1}{1}\]
\[-3=5-y1\]
Now bring the y1 to the left hand side and the -3 to the right hand side.
\[y1= 5+3 = 8\]

Answer 8

THANK YOU! & I have another question im pretty sure the answer is neither but im not sure.. Save

Determine if the lines that pass through the given points are parallel, perpendicular or neither. Line A: (5, 10) and (12, 6) Line B: (-2, 4) and (5, 8)

Answer 9

parallel would mean they have the same gradient
perpendicular meaning m1 x m2 = -1
so if the gradient of them both multiply to equal -1 they are perpendicular
neither means they both have different gradients.

Answer 10

@JayDS is neither correct?

Answer 11

You need to first find the slope of Line A and of Line B. Then you can compare those two slopes as JayDS suggests.

Answer 12

I did that, I got -4/7 & 4/7 so its neither???

Answer 13

Correct!
(This is my first day on this site, so I hope my input has been helpful?) :-)

Answer 14

It has been! thank you.

Answer 15

Can you help me with this one?
Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6).

Answer 16

neither is correct for the previous question.

Answer 17

for your next question.
slope intercept form is y=ax +b
so they give you an equation y=-4x m1=-4
perpendicular rule, if you remember, I mentioned it above.
m1 x m2 = -1
-4 x m2 = -1
m2 = 1/4
m2 is the gradient of the other line perpendicular to y=-4x

now we have m2=1/4 and a point (2,6)
we can substitute all the given information into the slope intercept form y=ax + b to find the value of b
6= 1/4(2) + b
6 = 2/4 + b
b = ......

now re-write the whole equation with the b value, it should look something like this.
y= 1/4x + b
replace the b with the value that you found as b above.

Answer 18

and also when you have a new question you should make a new post.

Answer 19

So the answer = y = 1/4 + 12 ?

Answer 20

I believe your b value is wrong.

Answer 21

but you have 6 = 2/4 + b so you would do 6 divided by 2/4 to get b right?

Answer 22

nevermind its minues on each side. My bad. so b is 5.5

Answer 23

yeh, I think it should be minus on both sides, maybe I am wrong lol.

Answer 24

6 = b + 2/4
b= 6 - 2/4
I think I should be right.

Answer 25

okay thanks

Answer 26

no problem, Isabell, I can call you that right?