Question

Which of these points on the line describes by the equation below?

y-5=6(x-7)

(7,5)
(-7,-5)
(-5,-7)
(5,7)

Answer 1

To determine which of the given points lies on the line described by the equation \( y - 5 = 6(x - 7) \), we can rearrange the equation into slope-intercept form (y = mx + b) and then see if the points satisfy the equation.

Starting with:
\[
y - 5 = 6(x - 7)
\]

We can expand and simplify:
\[
y - 5 = 6x - 42
\]
\[
y = 6x - 42 + 5
\]
\[
y = 6x - 37
\]

Now, we can test each of the given points to see if they satisfy the equation \( y = 6x - 37 \).

1. **Point (7, 5)**:
\[
y = 6(7) - 37 = 42 - 37 = 5 \quad \text{(satisfies the equation)}
\]

2. **Point (-7, -5)**:
\[
y = 6(-7) - 37 = -42 - 37 = -79 \quad \text{(does not satisfy the equation)}
\]

3. **Point (-5, -7)**:
\[
y = 6(-5) - 37 = -30 - 37 = -67 \quad \text{(does not satisfy the equation)}
\]

4. **Point (5, 7)**:
\[
y = 6(5) - 37 = 30 - 37 = -7 \quad \text{(does not satisfy the equation)}
\]

The only point that lies on the line is:

**(7, 5)**.