Question

been doing summer school but i only got two hours to get my grade up before they erase the points unless i meet my mark and ive been struggling with graphs so short explaination and answer would be appreciated

https://static.k12.com/eli/bb/501/4_26549/2_18873_10_26559/f9e4a9b50b005170ab8ce94c263639d6c7e52279/media/9279f7506abd6849457a15f43e7af82b700db897/mediaasset_964541_1.jpg

The lines are perpendicular.
The lines are parallel.
The lines have the same slope.
The lines have opposite reciprocal slopes.

Answer 1

they are obviously not parallel, and parallel lines have equal slopes, so cross out option 2 and 3

Answer 2

so you think it would be 1 and 4?

Answer 3

i think its 1 but its better we solve it first to get the exact answer

Answer 4

they are many ways to go about this

Answer 5

we could look for two points were each of the lines pass through and use them to get the gradient

Answer 6

the gold line passes through point (0,1) and (-1,3). You can then use the formula to find the gradient\[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 7

Our y2 is the 3 and our y1 is the 1, while our x2 is the -1 and our x1 is the 0

Answer 8

You can also do the same for the second equation

Answer 9

The green line passes through points (0,-3) and (2,-2)

Answer 10

Again your y2 here is -2 , y1 is -3, x2 is 2 and x1 is 0.

Answer 11

oh okay i think im getting it a bit

Answer 12

Then last of all, if two lines are perpendicular, the product of their slopes will be -1. If they are, then that means that they are perpendicular

Answer 13

so you think its just perpendicular ?

Answer 14

i dont know, i havent solved it, but if the product of their slopes is -1 then they are

Answer 15

Let me check

Answer 16

Yep

Answer 17

you'll get that the first gradient is -2 and the second is 1/2 and their product is -1

Answer 18

i got it right:) thank you