If the linear function given by the
rule 𝑓 of 𝑥 is equal to negative three 𝑥 plus 12 is represented by a straight
line, at which point does it intersect the 𝑦-axis?
We begin by recalling that any
linear function can be written in the form 𝑓 of 𝑥 is equal to 𝑚𝑥 plus 𝑏, where
𝑚 is the slope of the graph of the function and 𝑏 is the 𝑦-intercept. This is the 𝑦-coordinate of the
point at which the graph of the function crosses the 𝑦-axis.
In this question, we have the
linear function 𝑓 of 𝑥 is equal to negative three 𝑥 plus 12. The value of 𝑏, the 𝑦-intercept,
is therefore equal to 12. We could also work this out by
calculating 𝑓 of zero, as the graph of the function intersects the 𝑦-axis when 𝑥
is equal to zero. Negative three multiplied by zero
plus 12 is equal to 12. Using either of these methods, we
can conclude that the coordinates of the point where the graph of the function
intersects the 𝑦-axis is zero, 12.