Finding Linear Function through Two Points
To determine the linear function that goes through the points (3, -9) and (5, 13), we will use the slope-intercept form of a line, which is y = mx + b. Here, 'm' is the slope and 'b' is the y-intercept.
First, calculate the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1) = (13 - (-9)) / (5 - 3) = 22 / 2 = 11
Now we have the slope, which is 11. Next, we use one of the points to find the y-intercept (b). Let's use point (3, -9) and substitute x and y into the equation along with our slope:
-9 = 11 * 3 + b
-9 = 33 + b
b = -9 - 33
b = -42
Our linear function is y = 11x - 42.
