Question

Wright a linear function f with the values f(1)=1 and f(-3)=17

Answer 1

The linear function with f(1) = 1 and f(-3) = 17 is determined by finding the slope using the two points, resulting in a slope of -4. Using point-slope form and simplifying, the function is f(x) = -4x + 5.

Step-by-step explanation:

To write a linear function f with the given values f(1) = 1 and f(-3) = 17, we first need to determine the slope of the line. The slope m can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. Substituting the given values, we have:

m = (17 - 1) / (-3 - 1) = 16 / -4 = -4

Now that we know the slope is -4, we can use the point-slope form to write the function, which is y - y1 = m(x - x1). Substituting one of the given points and the slope, let's use the point (1, 1):

y - 1 = -4(x - 1)

Simplifying this equation, we get:

y = -4x + 4 + 1

y = -4x + 5

So the linear function f that satisfies the given conditions is f(x) = -4x + 5.

Answer 2

The linear function f(x) = -4x + 5 meets the criteria specified by the given function values.

To write a linear function f with the given values f(1) = 1 and f(-3) = 17, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, determine the slope (m):

m = (change in y) / (change in x)

Using the given points (1, 1) and (-3, 17):

m = (17 - 1) / (-3 - 1) = 16 / -4 = -4

Now that we have the slope, we can use either point to find the y-intercept (b). Let's use (1, 1):

1 = (-4)(1) + b

b = 1 + 4 = 5

The linear function f(x) is then:

f(x) = -4x + 5

This function satisfies the given conditions, with f(1) = 1 and f(-3) = 17.