What is an equation of the line that passes through the points left bracket, 0, comma, minus, 8, right bracket
(
0
,
−
8
)
(0,−8) and left bracket, minus, 8, comma, 2, right bracket
(
−
8
,
2
)
(−8,2)?
To find the equation of the line passing through the points (0, -8) and (-8, 2), we first need to find the slope of the line.
The formula to find the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points, we have:
m = (2 - (-8)) / (-8 - 0)
m = (2 + 8) / (-8)
m = 10 / -8
m = -5/4
Now that we have the slope, we can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)
We can choose either point to substitute into the equation. Let's use (0, -8):
y - (-8) = -5/4(x - 0)
Simplifying this equation, we get:
y + 8 = -5/4x
Then, we can rearrange it to the standard form of a linear equation, which is Ax + By = C:
5/4x + y + 8 = 0
Multiplying both sides by 4 to eliminate the fraction, we have:
5x + 4y + 32 = 0
So, the equation of the line passing through the points (0, -8) and (-8, 2) is 5x + 4y + 32 = 0.
To find the equation of the line passing through the points (0, -8) and (-8, 2), we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Find the slope (m)
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 two given points.
Using the points (0, -8) and (-8, 2):
m = (2 - (-8)) / (-8 - 0)
m = 10 / -8
m = -5/4
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can substitute the coordinates of one of the points into the equation. Let's use the point (0, -8):
-8 = (-5/4)(0) + b
-8 = b
Step 3: Write the equation
We now have the slope (m = -5/4) and the y-intercept (b = -8). Substitute these values into the slope-intercept form equation:
y = (-5/4)x - 8
Therefore, the equation of the line passing through the points (0, -8) and (-8, 2) is y = (-5/4)x - 8.
To find an equation of the line that passes through two given points, we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Step 1: Find the slope (m):
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (0, -8) and (-8, 2), we can substitute the values into the slope formula:
m = (2 - (-8)) / (-8 - 0)
m = (2 + 8) / (-8)
m = 10 / (-8)
m = -5/4
Step 2: Find the y-intercept (b):
To find the y-intercept (b), we can choose either of the given points and substitute its coordinates into the slope-intercept form (y = mx + b). Let's use the point (0, -8):
-8 = (-5/4)(0) + b
-8 = 0 + b
b = -8
Step 3: Write the equation:
Using the slope (m = -5/4) and y-intercept (b = -8), we can write the equation of the line:
y = (-5/4)x - 8
Therefore, the equation of the line passing through the points (0, -8) and (-8, 2) is y = (-5/4)x - 8.