Find the coordinates of two points on the line with the given equation y = -3x + 11, and hence, find its slope?
A straight line is a figure formed when two points are connected having the shortest distance between them, and both the ends extended to infinity. It is one of the most important concepts in geometry.
Answer: The slope of the line y = -3x + 11 is -3, which is found out from the points (0, 11) and (1, 8).
Let's understand the solution in detail.
To find two points on the line y = -3x + 11:
First, substitute x = 0, and find its corresponding y-coordinates.
Hence, the point (0, 11) lies on the line.
Then, substitute x = 1, and find its corresponding y-coordinates.
Hence, the point (1, 8) lies on the line.
Now, using the slope formula (y2 - y1) / (x2 - x1), we find the slope using the two points.
Hence, slope m = (11 - 8) / (0 - 1) = -3, which can be verified from the given equation.