Answer:
y = x + 6
Explanation:
Given two points on a line, we can find the equation of the line in slope-intercept form, whose general equation 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 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 substitute (-2, 4) for (x1, y1) and (2, 8) for (x2, y2):
m = (8 - 4) / (2 - (-2))
m = (4) / (2 + 2)
m = 4 / 4
m = 1
Thus, the slope is 1.
Step 2: Find b, the y-intercept:
Now we can find b, the y-intercept, by substituting (-2, 4) for (x, y) and 1 for m in the slope-intercept form:
4 = 1(-2) + b
(4 = -2 + b) + 2
6 = b
Thus, the y-intercept is 6.
Step 3: Write the equation in slope-intercept form:
Therefore, y = x + 6 is the equation of the line passing through the points (-2, 4) and (2, 8).