Which point is located on the line represented by the equation y+4=−5(x−7)
?
Responses
(4, -7)
(4, -7)
(-4, 7)
(-4, 7)
(-7, 4)
(-7, 4)
(7, -4)
To find the point located on the line represented by the equation, we need to solve the equation for x and y.
Starting with the equation y + 4 = -5(x - 7), let's isolate y.
First, distribute -5 to x and -7:
y + 4 = -5x + 35
Next, subtract 4 from both sides:
y = -5x + 31
Now we have the equation in slope-intercept form, y = mx + b, where m represents the slope and b the y-intercept.
Comparing this equation to the slope-intercept form, we have:
m = -5 and b = 31
From this equation, we can see that the line has a slope of -5 and a y-intercept of 31.
Let's test each given point to see if it satisfies the equation:
1. (4, -7)
Plugging in x = 4 and y = -7 into the equation:
-7 + 4 = -5(4 - 7)
-3 = -5(-3)
-3 = 15
This point does not satisfy the equation.
2. (-4, 7)
Plugging in x = -4 and y = 7 into the equation:
7 + 4 = -5(-4 - 7)
11 = -5(-11)
11 = 55
This point also does not satisfy the equation.
3. (-7, 4)
Plugging in x = -7 and y = 4 into the equation:
4 + 4 = -5(-7 - 7)
8 = -5(-14)
8 = 70
This point does not satisfy the equation.
4. (7, -4)
Plugging in x = 7 and y = -4 into the equation:
-4 + 4 = -5(7 - 7)
0 = -5(0)
0 = 0
This point satisfies the equation.
Therefore, the point located on the line represented by the equation y + 4 = -5(x - 7) is (7, -4).
y+4=−5(x−7)
y = -4 - 5 x +35
y = -5 x + 31
if x = -4, y = 51
oh we need a big positive x
if x = 7
y = -35 + 31 = -4
so (7 , -4) works
Apologies for the oversight in the previous response. You are correct.
By substituting x = 7 into the equation y = -5x + 31, we have:
y = -5(7) + 31
y = -35 + 31
y = -4
Thus, the correct point located on the line represented by the equation y + 4 = -5(x - 7) is (7, -4).
To find which point is located on the line represented by the equation y + 4 = -5(x - 7), we can start by rearranging the equation into the standard form of a linear equation, which is y = mx + b.
First, let's simplify the given equation:
y + 4 = -5(x - 7)
y + 4 = -5x + 35
y = -5x + 35 - 4
y = -5x + 31
Now that we have the equation in standard form, we can compare it to the general equation y = mx + b, where m represents the slope and b represents the y-intercept.
In our equation, the coefficient of the x-term is -5, so the slope (m) is -5.
From the given options, we need to find a point that lies on the line represented by the equation y = -5x + 31.
Let's substitute the x and y values from each given option into the equation and see which point satisfies it:
Option (4, -7):
When x = 4, y = -5(4) + 31 = -20 + 31 = 11. So, for this option, the point (4, -7) does not satisfy the equation.
Option (-4, 7):
When x = -4, y = -5(-4) + 31 = 20 + 31 = 51. So, for this option, the point (-4, 7) does not satisfy the equation.
Option (-7, 4):
When x = -7, y = -5(-7) + 31 = 35 + 31 = 66. So, for this option, the point (-7, 4) does not satisfy the equation.
Option (7, -4):
When x = 7, y = -5(7) + 31 = -35 + 31 = -4. So, for this option, the point (7, -4) satisfies the equation.
Therefore, the correct point located on the line represented by the equation y + 4 = -5(x - 7) is (7, -4).