Find the linear function with the following properties

Question

f(0)=5

slope of f =1

Answer 1

Remember that one way to represent a linear function is:

y = mx + b

where m is the slope, b is the y-intercept, and (x,y) is a point on the line.

We are given slope in the question (slope of f = 1) so we know that m = 1. Let's plug it in!

y = 1x + b

Now, we need to find b. From the question, we are given f(0) = 5. This means that when we plug in 0 for x, we get y = 5. Let's plug it in and solve for b!

(5) = 1(0) + b

5 = 0 + b

5 = b

So, b = 5! Let's put it all together.

y = 1x + 5 OR y = x + 5.

Answer 2

f(0) means "what do you get when you plug in 0 for x"" (loosely speaking).

Every point on the y-axis has the x-coordinate equal to 0. (Sketch this to see if you believe this is true.)

Graphs of linear functions are lines that intersect the y-axis. So, the point on the line when x = 0 is the y-intercept of the line.

Since you now know f(0) = the y-intercept = 5, and they told you the slope, you can write the equation for this linear function in slope-intercept form.

y = mx + b [where m = slope and b = y-intercept]