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( 6)= 8 ⇔ ( 6, 8)
f( 9)= 3 ⇔ ( 9, 3)
Let's use the given points to calculate m and b. We will start by substituting the points into the Slope Formula.
A slope of - 53 means that for every 3 horizontal steps in the positive direction, we take 5 vertical steps in the negative direction. Now that we know the slope, we can write a partial version of the equation.
f(x)= -5/3 x+ b
To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 6, 8).
