What is an equation of the line that passes through the points left bracket, 6, comma, 2, right bracket
(
6
,
2
)
(6,2) and left bracket, 8, comma, 0, right bracket
(
8
,
0
)
(8,0)?
To find the equation of the line passing through the points (6,2) and (8,0), we need to find the slope and then use the point-slope form or the slope-intercept form.
The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
So, let's calculate the slope first:
m = (0 - 2) / (8 - 6)
m = -2 / 2
m = -1
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting in one of the given points (6,2):
y - 2 = -1(x - 6)
y - 2 = -x + 6
y = -x + 8
Therefore, the equation of the line passing through the points (6,2) and (8,0) is y = -x + 8.
To find the equation of the line passing through two given points, we can use the slope-intercept form of a line equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Given points: (6, 2) and (8, 0)
x1 = 6, y1 = 2, x2 = 8, y2 = 0
m = (0 - 2) / (8 - 6)
m = -2 / 2
m = -1
The slope (m) is -1.
Now, we can substitute one of the points (let's use (6,2)) and the slope (m) into the slope-intercept form (y = mx + b) to find the value of b.
Using (6, 2):
y = mx + b
2 = -1(6) + b
2 = -6 + b
2 + 6 = b
b = 8
The y-intercept (b) is 8.
Now we can write the equation of the line:
y = -x + 8
Therefore, the equation of the line passing through the points (6,2) and (8,0) is y = -x + 8.
To find the equation of the line that passes through two points, you can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1),
where (x1, y1) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any point on the line.
Step 1: Calculate the slope:
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the given points.
Using the points (6, 2) and (8, 0), we have:
m = (0 - 2) / (8 - 6) = -2 / 2 = -1.
Step 2: Choose one of the given points:
Let's choose (6, 2) as our reference point.
Step 3: Substitute the values into the point-slope form:
Using the chosen point (6, 2) and the slope we found in Step 1 (-1), the equation becomes:
y - 2 = -1(x - 6).
Simplifying the equation further:
y - 2 = -x + 6.
Step 4: Rearrange the equation:
To express the equation in the standard form (Ax + By = C), we need to rearrange the terms:
x + y = 6 - 2.
Simplifying again:
x + y = 4.
Therefore, the equation of the line that passes through the points (6, 2) and (8, 0) is x + y = 4.