Given that the line y=ax+b passes through the points A(-1,7)and B(3,-1)), how do I find the values of a and b?

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joaobezerra joaobezerra · Answer 1 · 2022-08-26T17:44:43+02:00

The coefficients a and b for the linear function are given by:

a = -2, b = 5.

A linear function is modeled by:

y = ax + b

In which:

a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Given two points, the slope is given by change in y divided by change in x, hence, for points AB:

a = (-1 - 7)/(3 - (-1)) = -8/4 = -2.

Hence:

y = -2x + b.

When x = -1, y = 7, hence the value of b is found as follows:

7 = -2(-1) + b

b = 5.

More can be learned about linear functions at https://brainly.com/question/24808124

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