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 three points in function notation. Now, we need 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( -4)= -2 ⇔ ( -4, -2)
f( -2)= -1 ⇔ ( -2, -1)
f( 0)= 0 ⇔ ( 0, 0)
Let's use the first two given points to calculate m. We will start by substituting the points into the Slope Formula.
A slope of 12 means that for every 2 horizontal steps 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)= 1/2x+ b
To complete the equation, we also need to determine the y-intercept, b. Since we know that one of the given points is (0, 0) we already know that we have a y-intercept of 0. We can now complete the equation.
f(x)= 1/2x+( 0) ⇒ f(x)=1/2x
