Write an equation for the graph shown in the form y=ax+b.
I know I have to use the y=mx+b equation but I don't know how
m is the slope of the line. That's the distance it goes vertically divided by the distance it goes horizontally.
In this case, using known points, the vertical distance is (+2) – (0) = +2
In this case, using known points, the horizontal distance is (+5) – (–5) = +10
So the slope, which is conventionally called "m" is 0.2
b is the y-intercept of the line. That the point where the line crosses the y-axis.
Looking at the graph, it appears that the y-intercept is at (0,1)
So the y-intercept, which is conventionally called "b" is 1.
Plugging the values into y = mx + b, we find the equation to be y = 0.2x + 1 tentatively
Sometimes it isn't as straightforward, so plug in those two known values of x to see if it works.
When x = –5, does y = 0.2x + 1 equal 0 ? (0.2 • –5) + 1 = (–1) + (+1) = 0 so yes
When x = +5, does y = 0.2x + 1 equal 2 ? (0.2 • +5) + 1 = (+1) + (+1) = 2 so yes