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

Question

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): $$y=6(7)-37=42-37=5\text{(satisfies the equation)}$$

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

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

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

The only point that lies on the line is:

(7, 5).