An equation in slope-intercept form follows a specific format. In this case, we are asked to write our equation in function notation.
f(x)= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. We have also been given two points in function notation. To write these points as coordinate pairs, remember that the input x is the x-coordinate and the output f(x) is the y-coordinate.
f( x)= y ⇔ ( x, y)
f( 0)= 2 ⇔ ( 0, 2)
f( 2)= 4 ⇔ ( 2, 4)
Let's use the given points to calculate m. We will start by substituting the points into the Slope Formula.
A slope of 1 means that for every 1 horizontal step in the positive direction, we take 1 vertical step in the positive direction. Now that we know the slope, we can write a partial version of the equation.
f(x)= 1x+ b
To complete the equation, we also need to substitute the y-intercept, b. We can see that one of our given points, (0, 2), lies on the y-axis. Since the line crosses the y-axis at this point, we know the y-intercept and can complete the equation.
f(x)= 1x+ 2 ⇒ f(x)=x+2
