Which equations in point-slope form represent this line?
Select three that apply.
X Y
-6 -10
-4 -9
6 -4
The point-slope form of the equation of a line is:
y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
To find the equation of the line, we need to find the slope (m) and any point (x1, y1) on the line. Let's calculate the slope using the given points:
Point 1: (-6, -10)
Point 2: (-4, -9)
m = (y2 - y1) / (x2 - x1)
m = (-9 - (-10)) / (-4 - (-6))
m = (-9 + 10) / (-4 + 6)
m = 1 / 2
Now that we have the slope, let's find the equation of the line using one of the given points. Let's use Point 1: (-6, -10).
y - (-10) = 1/2(x - (-6))
y + 10 = 1/2(x + 6)
y + 10 = 1/2x + 3
y = 1/2x - 7
So, the equation of the line in point-slope form is y = 1/2x - 7.
Now let's check which other points satisfy this equation:
Point 3: (6, -4)
-4 = 1/2(6) - 7
-4 = 3 - 7
-4 = -4
The equation y = 1/2x - 7 is satisfied by Point 3 (6, -4).
Therefore, the three equations in point-slope form that represent this line are:
1. y = 1/2x - 7
2. y + 10 = 1/2(x + 6)
3. -4 = 1/2(6) - 7
To find the equations in point-slope form that represent the given line, we need to find the slope (m) and one point (x, y) on the line.
Let's choose two points (-6, -10) and (6, -4) to find the slope:
slope (m) = (change in y) / (change in x)
= (-4 - (-10)) / (6 - (-6))
= (-4 + 10) / (6 + 6)
= 6 / 12
= 1/2 or 0.5
Now that we have the slope, we can select three equations in point-slope form:
1. Using the point (-6, -10):
y - y1 = m(x - x1)
Substituting the values:
y - (-10) = 0.5(x - (-6))
y + 10 = 0.5(x + 6)
Answer: y + 10 = 0.5x + 3
2. Using the point (-4, -9):
y - y1 = m(x - x1)
Substituting the values:
y - (-9) = 0.5(x - (-4))
y + 9 = 0.5(x + 4)
Answer: y + 9 = 0.5x + 2
3. Using the point (6, -4):
y - y1 = m(x - x1)
Substituting the values:
y - (-4) = 0.5(x - 6)
y + 4 = 0.5(x - 6)
Answer: y + 4 = 0.5x - 3
Therefore, the three equations in point-slope form representing the given line are:
1. y + 10 = 0.5x + 3
2. y + 9 = 0.5x + 2
3. y + 4 = 0.5x - 3
To determine which equations in point-slope form represent a given line, we need to use the formula for point-slope form:
y - y1 = m(x - x1)
Where (x1, y1) represents a point on the line and m represents the slope of the line.
Let's calculate the slope (m) using the given points (-6, -10), (-4, -9), and (6, -4):
Slope (m) = (y2 - y1) / (x2 - x1)
For the points (-6, -10) and (-4, -9):
m = (-9 - (-10)) / (-4 - (-6))
= (-9 + 10) / (-4 + 6)
= 1 / 2
= 0.5
Now let's check the equations one by one using the calculated slope (m) and the given points:
1. Equation using point (-6, -10):
y - y1 = m(x - x1)
y - (-10) = 0.5(x - (-6))
y + 10 = 0.5(x + 6)
y + 10 = 0.5x + 3
This equation does not represent the line passing through the given points.
2. Equation using point (-4, -9):
y - y1 = m(x - x1)
y - (-9) = 0.5(x - (-4))
y + 9 = 0.5(x + 4)
y + 9 = 0.5x + 2
This equation does not represent the line passing through the given points.
3. Equation using point (6, -4):
y - y1 = m(x - x1)
y - (-4) = 0.5(x - 6)
y + 4 = 0.5(x - 6)
y + 4 = 0.5x - 3
This equation does not represent the line passing through the given points.
None of the equations in point-slope form from the given options represent the line passing through the points (-6, -10), (-4, -9), and (6, -4).