Answer:
Equation of the line: y = 2/5x - 3
Explanation:
The general equation of 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 first 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 (-5, -5) for (x1, y1) and (5, -1) for (x2, y2) in the slope formula:
m = (-1 - (-5)) / (5 - (-5))
m = (-1 + 5) / (5 + 5)
m = 4 / 10
m = 2/5
Thus, the slope of the line is 2/5.
Finding the y-intercept (b) and writing the equation of the line:
Now, we can find the y-intercept (b) by substituting (-5, -5) for (x, y) and 2/5 for m in the slope-intercept form:
-5 = 2/5(-5) + b
-5 = -10/5 + b
(-5 = -2 + b) + 2
-3 = b
Thus, the y-intercept of the line is -3.
Therefore, y = 2/5x - 3 is the equation of the line in slope-intercept form that passes through (-5, -5) and (5, -1).