Answer:
Equation with the given points: y = -3x + 30
Explanation:
Since we're given two points, we can find the equation of the line in slope-intercept form, whose general equation is given by:
y = mx + b, where:
- m is the slope,
- and b is the y-intercept.
Finding the slope (m):
We can find the slope using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where:
- m is the slope,
- (x1, y1) is one point on the line,
- and (x2, y2) is another point on the line.
Thus, we can find the slope of the line by substituting (3, 21) for (x1, y1) and (6, 12) for (x2, y2) in the slope formula:
m = (12 - 21) / (6 - 3)
m = -9 / 3
m = -3
Thus, the slope of the line is -3.
Finding the y-intercept and writing the equation of the line:
Now, we can find the y-intercept by substituting (3, 21) for (x, y) and -3 for m in the slope-intercept form:
21 = -3(3) + b
(21 = -9 + b) + 9
30 = b
Thus, the y-intercept of the line is 30.
Therefore, y = -3x + 30 is the equation of the line (in slope-intercept form) with the points (3, 21) and (6, 12).