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.
ok so im really bad at graphs could you kinda walk me through it
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?
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?
no this is usually where i get lost
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?
What is the value of y at that point?
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.
Do you know how to find the gradient of the line?
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?
How did you get that?
i moved 1 unit to the right then looked how may units it when't up/down. Im guessing i did that wrong
The actual gradient is -2 because moving to the right by 1 unit moves the line down by 2 units, can you see this?
So then can you write the equation of the line given what we've found out?
Not quite, you got the y-intercept and the gradient mixed up.
The equation of a line is y=(gradient)x +(y-intercept), which you'll often see as y=mx+c.
ok so the right way is Y=-2x+1
Yes :) Do you think you could apply this method to other questions like this now?
Cool :) if you have any problems don't hesitate to ask!
When is the function constant? X=_____to X=_____
A constant function is represented as a horizontal line on a graph.