Answer:
y = 5x - 11
Explanation:
General equation for the slope-intercept form:
The general equation for 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 (3, 4) for (x1, y1) and (2, -1) for (x2, y2) in the slope formula:
m = (-1 - 4) / (2 - 3)
m = (-5) / (-1)
m = 5
Thus, the slope (m) of the line is 5.
Finding the y-intercept (b):
Now we can find the y-intercept (b) of the line by plugging in 5 for m and (3, 4) for (x, y) in the slope-intercept form:
4 = 5(3) + b
(4 = 15 + b) - 15
-11 = b
Thus, the y-intercept (b) of the line is -11.
Compiling the equation in slope-intercept form:
Therefore, y = 5x - 11 is the equation of the line in slope-intercept form passing through (3, 4) and (2, -1).