Answer:
y = 4x - 14
Explanation:
Given two points that lie on a line, we can find the line's equation passing through the points in slope-intercept form, whose general equation is given by:
y = mx + b, where:
- m is the slope,
- and b is the y-intercept.
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Finding the slope (m):
We can find 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 on the line,
- and (x2, y2) is another point.
Thus, we can find the slope by substituting (4, 2) for (x1, y1) and (6, 10) for (x2, y2) in the slope formula:
m = (10 - 2) / (6 - 4)
m = 8 / 2
m = 4
Thus, the slope of the line is 4.
Finding the y-intercept (b):
Now we can find the y-intercept by substituting (4, 2) for (x, y) and 4 for m in the general equation of the slope-intercept form:
2 = 4(4) + b
(2 = 16 + b) - 16
-14 = b
Thus, the y-intercept of the line is -14.
Writing the equation of the line in slope-intercept form (y = mx + b):
Therefore, y = 4x - 14 is the equation of the line passing through the points (4, 2) and (6, 10)