find an equation of the line passing through the pair of points. write the equation in Ax+By=C (-9,7), (-10,-4)
Ax+By=C, (-9,7), (-10,-4)
m = (-4-7)/(-10-(-9))
m = 11
y -y1 = m (x -x1)
y -7 = 11(x -(-9)
y -7 = 11x +99
y -7 + 7 = 11x +99+7
y = 11x + 106
-11x + y = 106
To find the equation of a line passing through two given points, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Given points: (-9,7), (-10,-4)
Let's substitute the coordinates into the formula:
m = (-4 - 7) / (-10 - (-9))
m = (-4 - 7) / (-10 + 9)
m = (-11) / (-1)
m = 11
Step 2: Use the slope-intercept form of a linear equation and one of the given points to find the y-intercept (b).
Using the point (-9,7):
y = mx + b
7 = 11(-9) + b
7 = -99 + b
b = 106
Step 3: Write the equation in the form Ax + By = C.
Rearranging the equation from step 2:
11x + y = 106
Thus, the equation of the line passing through the points (-9,7) and (-10,-4) is 11x + y = 106.
To find the equation of the line passing through the points (-9,7) and (-10,-4), you can start by finding the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we get:
m = (-4 - 7) / (-10 - (-9))
= (-4 - 7) / (-10 + 9)
= (-11) / (-1)
= 11
Next, we can choose one of the points (let's use (-9,7)) and substitute the coordinates and the slope into the point-slope form of a line:
y - y1 = m(x - x1)
Using the point (-9, 7), we can substitute x1 = -9, y1 = 7, and m = 11:
y - 7 = 11(x - (-9))
y - 7 = 11(x + 9)
Now, let's simplify this equation:
y - 7 = 11x + 99
Finally, let's rearrange the equation into the standard form Ax + By = C:
11x - y = -99 + 7
11x - y = -92
Therefore, the equation of the line passing through the points (-9,7) and (-10,-4) in the standard form Ax + By = C is 11x - y = -92.