What is an equation of the line that passes through the points left bracket, minus, 8, comma, 1, right bracket(−8,1) and left bracket, minus, 7, comma, 0, right bracket(−7,0)?
The equation of the line passing through the points (-8,1) and (-7,0) can be found using the slope-intercept form equation y = mx + b, where m is the slope and b is the y-intercept.
First, find the slope:
m = (y2 - y1) / (x2 - x1)
m = (0 - 1) / (-7 - (-8))
m = (-1) / (-7 + 8)
m = (-1) / 1
m = -1
Now, substitute the slope into the equation:
y = -x + b
Using one of the given points (-8,1), substitute the x and y values:
1 = -(-8) + b
1 = 8 + b
b = 1 - 8
b = -7
The equation of the line that passes through the points (-8,1) and (-7,0) is y = -x -7.
To find the equation of the line that passes through the given points (-8,1) and (-7,0), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Calculate the slope (m):
The formula for finding the slope given two points is: m = (y2 - y1) / (x2 - x1).
Using the coordinates (-8,1) and (-7,0), we have:
m = (0 - 1) / (-7 - (-8))
m = -1 / (7 - 8)
m = -1 / -1
m = 1
Step 2: Use the slope and one point to find the y-intercept (b):
We can choose either point, let's use (-8,1).
Using the slope-intercept form, we have:
1 = 1 * (-8) + b
1 = -8 + b
b = 1 + 8
b = 9
Step 3: Write the equation:
Now that we have the slope (m = 1) and the y-intercept (b = 9), we can substitute these values into the slope-intercept form: y = mx + b.
Therefore, the equation of the line is:
y = 1x + 9, which simplifies to: y = x + 9.
To find the equation of a line that passes through two given points, we can use the slope-intercept form of the equation: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
First, let's find the slope (m) of the line using the two given points (-8,1) and (-7,0). The slope can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, we have:
x1 = -8
y1 = 1
x2 = -7
y2 = 0
Using the slope formula:
m = (0 - 1) / (-7 - (-8))
m = -1 / (-7 + 8)
m = -1 / 1
m = -1
Now that we have the slope (m = -1), we can substitute it into the slope-intercept form equation (y = mx + b) along with one of the given points (-8,1) to solve for b.
1 = -1 * (-8) + b
1 = 8 + b
1 - 8 = b
-7 = b
Therefore, the y-intercept (b) is -7.
Now we have the slope (m = -1) and the y-intercept (b = -7), we can write the equation of the line:
y = -x - 7
So, the equation of the line that passes through the points (-8,1) and (-7,0) is y = -x - 7.