Answer:
y = 3x - 2
Explanation:
General equation of the slope-intercept form:
The general equation of the slope-intercept form 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.
Finding the slope (m):
We can find the slope (m) 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 (m) by substituting (2, 4) for (x1, y1) and (4, 10) for (x2, y2) in the slope formula:
m = (10 - 4) / (4 - 2)
m = 6/2
m = 3
Thus, the slope of the line is 3.
Finding the y-intercept (b):
Now we can find the y-intercept by substituting (2, 4) for (x, y) and 3 for m in the slope-intercept form:
4 = 3(2) + b
(4 = 6 + b) - 6
-2 = b
Thus, the y-intercept (b) is -2.
Determining the slope-intercept form of the line:
Thus, y = 3x - 2 is the equation of the line in slope-intercept form that passes through the points (2, 4) and (4, 10).