Question

F(-2)=1,f(1)=7 write a linear function

Answer 1

To find the linear function, we calculate the slope using the two points, finding it to be 2. Then, using one point to solve for the y-intercept, we find the y-intercept to be 5. The linear function is y = 2x + 5.

Step-by-step explanation:

To write a linear function that fits the given points, we need to first calculate the slope (m) using the given points (x1, y1) = (-2, 1) and (x2, y2) = (1, 7). The slope is calculated as follows:

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

m = (7 - 1) / (1 - (-2))

m = 6 / 3

m = 2

Now that we have the slope, we can use one of the points to solve for the y-intercept (b) using the formula y = mx + b. Let's use the point (-2, 1):

1 = 2(-2) + b

1 = -4 + b

b = 5

So, our linear equation is:

y = 2x + 5

This equation represents a line that passes through the points (-2, 1) and (1, 7), with a slope of 2 and a y-intercept of 5.