Question

If k is a constant and there is a function such that

x+y=k
with an x-intercept of at x = -1,

what is the equation of this function?

Answer 1

To find the equation of the function with the given conditions, we can start by finding the y-intercept and then use the x and y intercepts to write the equation.

Given: x + y = k

Since the x-intercept is at x = -1, this means the point (-1, 0) lies on the graph of the function.

To find the y-intercept, let x = 0:

0 + y = k

y = k

So, the y-intercept is (0, k).

Now, we have two points on the graph of the function: (-1, 0) and (0, k).

Using the two points, we can find the slope (m) of the function:

m = (k - 0) / (0 - (-1)) = k / 1 = k

The equation of the function in slope-intercept form is:

y = mx + b

Substituting the slope (m) and the y-intercept (b = k) into the equation:

y = kx + k

So, the equation of the function is y = kx + k.