Finding the y-intercept value b

Hi İzel, let's solve this problem together. We are given two points on a line and need to find the value of the constant b, which is related to the y-intercept.

First, let's look at the two points provided in the table. We have the coordinate pairs k comma thirteen and k plus seven comma negative fifteen.

To find the slope of the line, we use the formula rise over run, which is the change in y divided by the change in x.

Substituting our values in, the change in y is negative fifteen minus thirteen, and the change in x is the quantity k plus seven minus k.

Simplifying the denominator, the k values cancel out, leaving us with seven. In the numerator, negative fifteen minus thirteen is negative twenty-eight.

Finally, negative twenty-eight divided by seven gives us a slope of negative four.

Now, the problem states that the y-intercept of the line is the point k minus five comma b.

By definition, the y-intercept occurs where the x-coordinate is zero. This means k minus five must equal zero.

Solving for k, we add five to both sides and find that k equals five.

If k is five, we can find the actual coordinates of the points in our table. The first point p one was k comma thirteen, which becomes five comma thirteen.