Answer: y=-9x+6
Step-by-step explanation: The common form of a line is the Slope-Intercept form which is y=Mx+B. M represents the slope of the line, B represents the y-intercept, and x and y represent a point on the xy plane such as (1,2). The y-intercept is the point at which x = 0. The slope of a line is given by the equation (y2-y1)/(x2-x1) where (y1,x1) and (y2,x2) are points on a coordinate plane.
In this problem, we are already given M or the slope which is -9. We are also given the y-intercept but it's not as clear. f(x)=y represents a general function where you input an x-coordinate x into f(x) and the function produces a y-coordinate y. If we had a function f(x)=2x+1 and we input 3 as x we replace all the x's with 3 which gives us f(x)=2(3)+1=7. f(3)=7 which can be written as (3,7) being a point on the function. Lines in the coordinate plane represent linear functions because they have a constant slope due to no exponents.
Here, we are told f(0)=6 which can be rewritten as (0,6) being a point on the linear function. I said earlier that the y-intercept is when x=0 and this point has x=0. y=6 when x=0 so 6 is our y-intercept. Now we plug into the slope-intercept form y=mx+b giving us y=-9x+6 which is our answer.
Hope this helps! For practice, find the linear function that has the two points (1,2) and (3,6) on it.