Question

Complete the equation of the linear function.
Y=_______X+_______

Answer 1

http://static.k12.com/calms_media/media/1524000_1524500/1524412/1/4ca0974cc0b94f0ca087c628d4c99d7f088b0730/MS_IMC-140901-106145.jpg

Answer 2

The equation y=mx+c intersects the y-axis at y=c and has a gradient of m. You can either determine this by looking at the graph and seeing how far the line moves per unit in the x-direction, or you can try particular x.

e.g. When x=0, y=c
and when x=1, y=m+c.
Comparing with points on the graph give m and c.

Answer 3

ok so im really bad at graphs could you kinda walk me through it

Answer 4

Sure. So do you know that for a line y=mx+c, m is the gradient of the line and c is the y-intercept of the line?

Answer 5

yeah

Answer 6

So if you look at the graph, you know that c is equal to the value of y when the line intersects the y-axis. In other words, it's the value when x=0. Can you say what that is from the diagram?

Answer 7

no this is usually where i get lost

Answer 8

So the y-axis is the vertical line in the middle of the graph. Do you see where the line you're given crosses it?

Answer 9

yeah

Answer 10

What is the value of y at that point?

Answer 11

1?

Answer 12

Yep. So that's your y-intercept, so now we know the line looks like y=mx+1. Now all we need to do is to find m.

Answer 13

Do you know how to find the gradient of the line?

Answer 14

no

Answer 15

Okay. So the gradient (which is m) is essentially how much the line moves up/down when you go to the right by one square (unit). Can you tell what this is from the graph?

Answer 16

4?

Answer 17

How did you get that?

Answer 18

i moved 1 unit to the right then looked how may units it when't up/down. Im guessing i did that wrong

Answer 19

The actual gradient is -2 because moving to the right by 1 unit moves the line down by 2 units, can you see this?

Answer 20

yeah

Answer 21

So then can you write the equation of the line given what we've found out?

Answer 22

Y=1X+-2

Answer 23

Not quite, you got the y-intercept and the gradient mixed up.

Answer 24

The equation of a line is y=(gradient)x +(y-intercept), which you'll often see as y=mx+c.

Answer 25

ok so the right way is Y=-2x+1

Answer 26

Yes :) Do you think you could apply this method to other questions like this now?

Answer 27

yeah

Answer 28

Cool :) if you have any problems don't hesitate to ask!

Answer 29

k

Answer 30

When is the function constant?
X=_____to X=_____

Answer 31

http://static.k12.com/calms_media/media/1524000_1524500/1524416/1/411ba68c64d77faa64f19231dbddc8c7ba7e16fa/MS_IMC-140901-106149.jpg

Answer 32

A constant function is represented as a horizontal line on a graph.