What is the equation of a line that passes through the points (0, 9) and (3, 0)?

To find the equation of a line that passes through two points, we can use the slope-intercept form of the equation of a line, which is given by:

y = mx + b

Where:

• m is the slope of the line
• b is the y-intercept of the line

First, we need to calculate the slope (m) using the coordinates of the two given points: (0, 9) and (3, 0). The formula for calculating the slope between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ – y₁) / (x₂ – x₁)

Substituting the coordinates:

m = (0 – 9) / (3 – 0) = -9 / 3 = -3

Now that we have the slope, we can substitute one of the points into the slope-intercept form to find the y-intercept (b). Let’s use the point (0, 9):

9 = -3(0) + b

This simplifies to:

b = 9

Now we have both components of our equation:

• Slope (m) = -3
• y-intercept (b) = 9

Thus, we can write the equation of the line:

y = -3x + 9

To summarize, the equation of the line that passes through the points (0, 9) and (3, 0) is:

y = -3x + 9