Answer:
Equation of the line in slope-intercept form: y = 2x - 3
Explanation:
The general equation of the sloe-intercept form of a line is given by:
y = mx + b, where
- (x, y) is any point on the line,
- m is the slope,
- and b is the y-intercept.
Step 1: Find m, the slope:
We can find m, the slope of the line using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where:
- m is the slope,
- (x1, y1) is one point,
- and (x2, y2) is another point.
Thus, we can plug in (2, 1) for (x1, y1) and (-1, -5) for (x2, y2) to find m, the slope of the line:
m = (-5 - 1) / (-1 - 2)
m = (-6) / (-3)
m = 2
Thus, the slope of the line is 2.
Step 2: Find b, the y-intercept of the line:
We can find b, the y-intercept of the line by plugging in any of the two points for (x, y) and 2 for m in the slope-intercept form. Let's use (2, 1) for (x, y):
1 = 2(2) + b
1 = 4 + b
-3 = b
Thus, the y-intercept of the line is -3.
Therefore, the equation of a line in slope-intercept form passing through the points (2, 1) and (-1, -5) is y = 2x - 3