Question

Find the linear function with the following properties.

f(−3)=−12
f(−7)=4

Answer 1

Answer:

f(x) = -4x - 24

Step by step Explanation:

To find the linear function f(x) with the given properties, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Using the two given points, we can find the slope of the line:

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

m = (4 - (-12)) / (-7 - (-3))

m = 16 / (-4)

m = -4

Now we have the slope of the line, and we can use one of the given points to find the y-intercept:

f(x1) = y1

f(-3) = -12

So when x = -3, y = -12. We can use this point to find the y-intercept:

y - y1 = m(x - x1)

y - (-12) = -4(x - (-3))

y + 12 = -4(x + 3)

y = -4x - 24

Therefore, the linear function f(x) that satisfies the given properties is:

f(x) = -4x - 24

Answer 2

To find the linear function with the given properties, we need to determine the slope and y-intercept of the function.

We can use the slope-intercept form of a linear function, which is:

y = mx + b

where m is the slope and b is the y-intercept.

First, we can find the slope using the two given points:

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

slope = (4 - (-12)) / (-7 - (-3))

slope = 16 / (-4)

slope = -4

Now that we have the slope, we can use one of the given points to find the y-intercept. Let's use the point (-3, -12):

y = mx + b

-12 = (-4)(-3) + b

-12 = 12 + b

b = -24

Therefore, the linear function that satisfies the given properties is:

f(x) = -4x - 24