What is the equation of the line that passes through the points (-2, 3) and (4, -1)?
To find the equation of a line passing through two points, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, you need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's assign the coordinates of the first point (-2, 3) as (x1, y1), and the coordinates of the second point (4, -1) as (x2, y2).
Using these values, the slope (m) becomes:
m = (-1 - 3) / (4 - (-2))
= (-4) / (4 + 2)
= -4 / 6
= -2 / 3
Now that we have the slope (m), we need to find the y-intercept (b). To do this, substitute the coordinates of one point into the slope-intercept form and solve for b.
Using the coordinates of the first point (-2, 3), substitute x = -2 and y = 3 into the equation:
3 = (-2/3) * (-2) + b
Simplify:
3 = 4/3 + b
To isolate b, subtract 4/3 from both sides:
3 - 4/3 = b
9/3 - 4/3 = b
5/3 = b
Now, we have the slope (m = -2/3) and the y-intercept (b = 5/3).
Substitute these values into the slope-intercept form, y = mx + b, to get the equation of the line:
y = (-2/3)x + 5/3
Therefore, the equation of the line that passes through the points (-2, 3) and (4, -1) is y = (-2/3)x + 5/3.
To find the equation of the line passing through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
1. Find the slope (m):
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-2, 3) and (4, -1):
m = (-1 - 3) / (4 - (-2))
m = (-4) / (6)
m = -2/3
2. Use one of the given points and the slope to find the y-intercept (b):
Using the point (-2, 3), substitute x = -2, y = 3, and m = -2/3 into the slope-intercept form.
3 = (-2/3)(-2) + b
3 = 4/3 + b
b = 3 - 4/3
b = 5/3
3. Write the equation using the slope and y-intercept:
The equation of the line passing through the points (-2, 3) and (4, -1) is y = (-2/3)x + 5/3.