Write the equation of the line passing through the points (−1, 2) and (3, 4)
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m) of the line passing through the points (-1, 2) and (3, 4), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates into the formula:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Now that we have the slope (m), we can proceed to find the y-intercept (b). We'll choose one of the given points, let's use (-1, 2), to substitute into the equation y = mx + b.
When x = -1 and y = 2:
2 = (1/2)(-1) + b
2 = -1/2 + b
3/2 = b
Finally, we can write the equation of the line passing through the points (-1, 2) and (3, 4) as:
y = (1/2)x + 3/2
To find the equation of a line passing through two points, we 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, we 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 to (x1, y1) and the coordinates of the second point to (x2, y2).
(x1, y1) = (-1, 2)
(x2, y2) = (3, 4)
Now, substituting the values into the slope formula:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Next, we can use one of the given points and the slope to find the y-intercept (b). Let's use the first point (-1, 2).
y = mx + b
2 = (1/2)(-1) + b
2 = -1/2 + b
We can simplify this equation:
2 + 1/2 = b
4/2 + 1/2 = b
b = 5/2
Now we can write the equation of the line using the slope-intercept form:
y = 1/2x + 5/2
Therefore, the equation of the line passing through the points (-1, 2) and (3, 4) is y = 1/2x + 5/2.
To write the equation of a line passing through two points, we can use the slope-intercept form of the equation: y = mx + b.
Step 1: Calculate the slope (m):
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (-1, 2) and (3, 4). So we have:
m = (4 - 2) / (3 - (-1))
= 2 / 4
= 1/2
Step 2: Find the y-intercept (b):
To find the y-intercept (b), we can use the point-slope form of the equation: y - y1 = m(x - x1). You can choose any of the two given points. Let's use (-1, 2):
y - 2 = (1/2)(x - (-1))
y - 2 = (1/2)(x + 1)
y - 2 = (1/2)x + 1/2
y = (1/2)x + 1/2 + 2
y = (1/2)x + 5/2
So, the equation of the line passing through the points (-1, 2) and (3, 4) is y = (1/2)x + 5/2.