Write a function representing the line that includes the points (3,3) and (-6, 15)
Find the slope and then solve for y=mx+b
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