Answer:
y = -3/2 + 4
Explanation:
Given two points through which a line passes, we can find its equation 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.
Thus, we can find the slope (m) by substituting (6, -5) for (x1, y1) and (-8, 16) for (x2, y2) in the slope formula:
m = (16 - (-5)) / (-8 - 6)
m = (16 + 5) / (-14)
m = 21 / -14
m = -3/2
Thus, the slope is -3/2.
Finding the y-intercept (b):
Now we can find the y-intercept (b) by substituting -3/2 for m and (6, -5) for (x, y) in the slope-intercept form:
-5 = -3/2(6) + b
-5 = -18/2 + b
(-5 = -9 + b) + 9
4 = b
Thus, the y-intercept is 4.
Writing the equation of the line in slope-intercept form:
Therefore, y = -3/2 + 4 is the equation of the line in slope-intercept that passes through (6, -5) and (-8, 16)