Question

Khalid is investigating two linear functions.The first linear function is defined by the equation2x+3y=12.The second linear function passes through the points(3,−2)and(−2,k). For the case where the two linear functions have the samey-intercept, what must be the value of k?

Answer 1

The value of k that makes the second linear function have the same y-intercept as the first linear function is -2.

Step-by-step explanation:

In order to find the value of k for the second linear function, we need to find the equation of the line that passes through the points (3, -2) and (-2, k). We can use the formula for the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Let's find the slope first:

m = (y2 - y1) / (x2 - x1)

m = (k - (-2)) / (-2 - 3)

m = (k + 2) / -5

Now we can substitute one of the points into the equation:

-2 - y1 = (k + 2) / -5 * (3 - x1)

Simplifying:

-2 + 2 = (k + 2) / -5 * (3 + 2)

0 = (k + 2) / -5 * 5

0 = (k + 2)

k = -2

Therefore, the value of k that makes the second linear function have the same y-intercept as the first linear function is -2.