Answer:
y = -3/2x + 3
Explanation:
General equation for the slope-intercept form:
The general equation for the slope-intercept form 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 on the line.
Since (-2, 6) and (-4, 9) are points on the line, we can find its slope by substituting (-2, 6) for (x1, y1) and (-4, 9) for (x2, y2) in the slope formula:
m = (9 - 6) / (-4 - (-2))
m = 3 / (-4 + 2)
m = 3 / -2
m = -3/2
Thus, the slope of the line is -3/2.
Finding the y-intercept:
The y-intercept is the y-coordinate when x = 0.
Since the y-coordinate when x = 0 is 3, its the y-intercept.
Determining the equation of the line in fully simplified slope-intercept form:
Therefore, the equation of the line in fully simplified slope-intercept form is given by:
y = -3/2x + 3