Answer:
y = 2x - 1.
Step-by-step explanation:
The equation of a linear function can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept. To find the equation of the linear function that passes through the points (3, 5) and (-3, -7), we need to determine the values of m and b.
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (3, 5) and (-3, -7), we have:
m = (-7 - 5) / (-3 - 3) = -12 / -6 = 2
So the slope (m) of the linear function is 2.
Next, we can use the slope-intercept form (y = mx + b) and substitute the coordinates of one of the given points to find the value of b.
Let's use the point (3, 5):
5 = 2(3) + b
Simplifying the equation:
5 = 6 + b
Now, solve for b:
b = 5 - 6 = -1
Therefore, the value of b is -1.
Now that we have the slope (m = 2) and the y-intercept (b = -1), we can write the equation of the linear function:
y = 2x - 1
So, the equation of the linear function that passes through the points (3, 5) and (-3, -7) is y = 2x - 1.
