# Write a function representing the line that includes the points (3,3) and (-6, 15)

## To find the equation of a line that includes two given points, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

First, let's find the slope (m) of the line using the formula:

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

Given points (3, 3) and (-6, 15):

m = (15 - 3) / (-6 - 3)
= 12 / -9
= -4/3

Now that we have the slope (m), we can substitute one of the points into the slope-intercept form to find the y-intercept (b). Let's use the point (3, 3):

3 = (-4/3)(3) + b
3 = -4 + b
b = 7

Therefore, the equation of the line that includes the points (3, 3) and (-6, 15) is:

y = (-4/3)x + 7

## To write a function representing a line that includes two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line, and b is the y-intercept.

To find the slope (m) of the line passing through the points (x₁, y₁) and (x₂, y₂), we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Given that the points are (3, 3) and (-6, 15), we substitute the values into the formula:

m = (15 - 3) / (-6 - 3)
m = 12 / -9
m = -4/3

Now that we have the slope, we can substitute it back into the slope-intercept form and solve for the y-intercept (b). Let's use the first point (3, 3):

3 = (-4/3)(3) + b

Multiply to simplify:

3 = -4 + b

Now, solve for b:

b = 3 + 4
b = 7

Therefore, the equation representing the line passing through the points (3, 3) and (-6, 15) is:

y = (-4/3)x + 7

## slope = (15-3)/(-6-3) = 12/-9 = -4/3

y - 3 = (-4/3)(x-3)
3y - 9 = -4x + 12
4x + 3y = 21