A line is shown on the coordinate plane.
On coordinate plane, points (2, 1), (1, 5) and (0, 9) are connected through a line.
Drag a number to each box to represent the equation of the line
To find the equation of the line passing through the points (2, 1), (1, 5), and (0, 9), we can use the slope-intercept form of the equation: y = mx + b, where m represents the slope, and b represents the y-intercept.
Step 1: Calculate the slope (m):
m = (y₂ - y₁) / (x₂ - x₁).
Using the points (2, 1) and (1, 5):
m = (5 - 1) / (1 - 2)
m = 4 / (-1)
m = -4
Step 2: Substitute a point (x, y) and the calculated slope (m) into the equation y = mx + b and solve for b.
Using the point (2, 1):
1 = -4(2) + b
1 = -8 + b
b = 9
Step 3: Write the equation of the line:
y = -4x + 9
So, the equation of the line passing through the points (2, 1), (1, 5), and (0, 9) is y = -4x + 9.