Which point is located on the line represented by the equation y + 4 = –5(x – 3)?
(1 point)
Responses
(–4, –5)
(–4, –5)
(–5, –4)
(–5, –4)
(3, –4)
(3, –4)
(–3, 4)
(–4, –5)
To determine which point is located on the line represented by the equation y + 4 = –5(x – 3), we need to substitute the given points into the equation and check which make the equation true.
Let's go through each option:
Option (–4, –5):
Substituting x = -4 and y = -5 into the equation:
-5 + 4 = -5(-4 - 3)
-1 = -5(-7)
-1 = 35
The equation is false, so (–4, –5) is not on the line.
Option (–5, –4):
Substituting x = -5 and y = -4 into the equation:
-4 + 4 = -5(-5 - 3)
0 = -5(-8)
0 = 40
The equation is false, so (–5, –4) is not on the line.
Option (3, –4):
Substituting x = 3 and y = -4 into the equation:
-4 + 4 = -5(3 - 3)
0 = 0
The equation is true, so (3, –4) is on the line.
Option (–3, 4):
Substituting x = -3 and y = 4 into the equation:
4 + 4 = -5(-3 - 3)
8 = 30
The equation is false, so (–3, 4) is not on the line.
Therefore, the point (3, -4) is located on the line represented by the equation.
are you sure
To find which point is located on the line represented by the equation, we can solve the equation by substituting values for x and y. The equation given is:
y + 4 = -5(x - 3)
Let's try substituting the coordinates of the given points and see which one satisfies the equation.
Option 1: (-4, -5)
Substituting x = -4 and y = -5 into the equation:
-5 + 4 = -5(-4 - 3)
-1 = -5(-7)
-1 = 35
Since -1 does not equal 35, the point (-4, -5) is not located on the line.
Option 2: (-5, -4)
Substituting x = -5 and y = -4 into the equation:
-4 + 4 = -5(-5 - 3)
0 = 40
Since 0 does not equal 40, the point (-5, -4) is not located on the line.
Option 3: (3, -4)
Substituting x = 3 and y = -4 into the equation:
-4 + 4 = -5(3 - 3)
0 = 0
Since 0 equals 0, the point (3, -4) is located on the line.
Option 4: (-3, 4)
Substituting x = -3 and y = 4 into the equation:
4 + 4 = -5(-3 - 3)
8 = -5(-6)
8 = 30
Since 8 does not equal 30, the point (-3, 4) is not located on the line.
Therefore, the point located on the line represented by the equation is (3, -4).