Answer:
y = 4x + 6
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 (-1, 2) for (x1, y1) and (3, 18) in the slope formula:
m = (18 - 2) / (3 - (-1))
m = 16 / (3 + 1)
m = 16 / 4
m = 4
Thus, the slope (m) is 4.
Finding the y-intercept (b) and writing the equation of the line in slope-intercept form:
Now we can find the y-intercept (b) by substituting 4 for m and (-1, 2) for (x, y) in the slope-intercept form:
2 = 4(-1) + b
(2 = -4 + b) + 4
6 = b
Thus, the y-intercept (b) is 6.
Therefore, y = 4x + 6 is the equation of the line passing through the points (-1, 2) and (3, ,18).