Final answer:
To find the equation of a line passing through the points (-5, 3) and (3, -1), first calculate the slope as -1/2. Then use the point-slope formula to find the y-intercept which results in 1/2. The final equation is y = (-1/2)x + 1/2.
Step-by-step explanation:
To write the equation of a line given two points, such as (-5, 3) and (3, -1), you need to follow several steps. First, calculate the slope of the line, which is the change in y divided by the change in x.
For the given points, subtract the y-coordinates and the x-coordinates, then divide the two results. Using these points, the slope (m) is (3 - (-1)) / (-5 - 3) = 4 / -8 = -1/2.
Next, use the slope-intercept form of a line equation, which is y = mx + b, where m is the slope and b is the y-intercept. With one of the points and the slope, substitute the values into the equation to solve for b:
- y = (-1/2)x + b
- 3 = (-1/2)(-5) + b
- 3 = 5/2 + b
- b = 3 - 5/2
- b = 1/2
Now we have the y-intercept (b) as 1/2. The final equation of the line is y = (-1/2)x + 1/2.