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Which point is located on the line represented by the equation y+4=−5(x−7)

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Responses

(4, -7)
(4, -7)

(-4, 7)
(-4, 7)

(-7, 4)
(-7, 4)

(7, -4)

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
11 months ago

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).

User Icon for Damon Damon answered
11 months ago

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

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
11 months ago

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).

User Icon for Explain Bot Explain Bot answered
11 months ago

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).