which equation represents the line that passses through the points (6, -3) and (-4, -9)
None of the above.
find the slope m
Then, use either point in the point-slope form of the line:
y-k = m(x-h)
where (h,k) is either (6,-3) or (-4,-9)
To find the equation of the line that passes through the points (6, -3) and (-4, -9), we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) are the coordinates of a point on the line and m is the slope of the line.
First, we need to find the slope (m) of the line using the coordinates of the two points:
m = (y₂ - y₁) / (x₂ - x₁)
Let's substitute the values using the coordinates of the given points:
m = (-9 - (-3)) / (-4 - 6)
= (-9 + 3) / (-4 - 6)
= -6 / -10
= 3/5
Now that we have the slope (m), we can choose either of the two points (6, -3) or (-4, -9) and substitute the values into the point-slope form equation to find the equation of the line.
Let's use the point (6, -3):
y - y₁ = m(x - x₁)
y - (-3) = (3/5)(x - 6)
y + 3 = (3/5)(x - 6)
y + 3 = (3/5)x - (3/5) * 6
y + 3 = (3/5)x - 18/5
Finally, let's simplify the equation:
y = (3/5)x - 18/5 - 3
y = (3/5)x - 18/5 - 15/5
y = (3/5)x - 33/5
So, the equation of the line that passes through the points (6, -3) and (-4, -9) is y = (3/5)x - 33/5.
To find the equation of a line that passes through two points, you can use the point-slope form of a linear equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents one of the points on the line, and 'm' represents the slope of the line.
First, let's find the slope (m) using the given points:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (6, -3) and (-4, -9):
m = (-9 - (-3)) / (-4 - 6)
m = (-9 + 3) / (-10)
m = -6 / -10
m = 3/5
Now, we can choose either point (6, -3) or (-4, -9) and the slope (3/5) to write the equation of the line.
Let's choose (6, -3):
y - y₁ = m(x - x₁)
y - (-3) = (3/5)(x - 6)
y + 3 = (3/5)(x - 6)
This is the equation of the line that passes through the points (6, -3) and (-4, -9).