Hi! I know this may be cheating but I just wanna ask if one of yall could tell me the answer just for these 3 questions, it would be a bunch of help! =,)

1. Write the equation in point-slope form of the line that passes through the given points. Then write in point-slope form. (−6,6) 𝑎𝑛𝑑 (3,3)

2. Are the graphs of the equations = −2 + 3 and 2 + = 7, parallel, perpendicular, or neither? Explain.

3. Determine whether this statement is always, sometimes, or never true. Two lines with the same slope and different y-intercepts are perpendicular.

1.

m = tan θ

m = ( y2 - y1 ) / ( x2 - x1)

In this case:

x1 = - 6 , y1 = 6

x2 = 3 , y2 = 3

m = ( y2 - y1 ) / ( x2 - x1)

m = ( 3 - 6 ) / [ 3 - ( - 6 ) ]

m = - 3 / ( 3 + 6 )

m = - 3 / 9

m = 3 ∙ ( - 1 ) / 3 ∙ 3

m = - 1 / 3

y - y1 = m ( x - x1 )

y - 6 = ( - 1 / 3 ) [ x - ( - 6 ) ]

y - 6 = ( - 1 / 3 ) ( x + 6 )

y - 6 = ( - 1 / 3 ) x + ( - 1 / 3 ) ∙ 6

y - 6 = ( - 1 / 3 ) x - 6 / 3

y - 6 = ( - 1 / 3 ) x - 2

Add 6 to both sides.

y = ( - 1 / 3 ) x + 4

2.

This as it is written means nothing.

3.

Two lines are parallel if they have both the same slope and different y-intercepts.

So two lines with the same slope and different y-intercepts are parallel.

Thank you sm Bosnian!! You have no idea how happy I am!! Thank u again!!!!

Hello! I'm here to help you with your questions. However, I won't just provide you with the answers. I will explain how to solve each question so that you can understand the process and learn from it. So, let's get started!

1. To write the equation in point-slope form of a line that passes through two given points, we need to use the formula:

𝑦 − 𝑦₁ = 𝑚(𝑥 − 𝑥₁)

where (𝑥₁, 𝑦₁) and (𝑥, 𝑦) are the coordinates of the given points, and 𝑚 is the slope of the line.

For the first question, we have the points (−6,6) and (3,3). To find the slope, we use the formula:

𝑚 = (𝑦₂ - 𝑦₁) / (𝑥₂ - 𝑥₁)

Substituting the values, we get:

𝑚 = (3 - 6) / (3 - (-6)) = -3 / 9 = -1/3

Now, we can choose any one of the given points and substitute the values into the point-slope form equation. Let's choose (−6,6):

𝑦 − 6 = (-1/3)(𝑥 − (-6))

Simplifying further:

𝑦 − 6 = (-1/3)(𝑥 + 6)

This is the equation in point-slope form.

2. To determine if the graphs of two equations are parallel, perpendicular, or neither, we need to compare their slopes. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other (i.e., their product equals -1), the lines are perpendicular. If neither of these conditions is met, the lines are neither parallel nor perpendicular.

Given the equations 𝑦 = −2𝑥 + 3 and 𝑦 = 2𝑥 + 7, we can see that the slopes of the two lines are -2 and 2, respectively. Since the product of -2 and 2 is -4 (not -1), the lines are neither parallel nor perpendicular.

3. Two lines are perpendicular if and only if the product of their slopes is -1. So, the statement "Two lines with the same slope and different y-intercepts are perpendicular" is sometimes true. It is true when the slope of the lines is -1. However, it is not true when the slope of the lines is any other value.

Remember, understanding the process and concepts behind these questions is more important than just knowing the answers. Feel free to ask if you have any further questions or need clarification on any step!