Answer:
1) y = -1/4x + 5.25
2) y = -2x + 11
3) x = -7/4, original statement is false
4) y = -2/15x
5) y = 2.5x + 2.5
Explanation:
Question one: To find the slope of a perpendicular line, use the formula y = (-1/m)x+ b. When having to pass through a certain point, you do not take the same b value, though. Since the original equation is y = 4x + 7, just plug in the 4 into the formula, and it should look like this: y = (-1/4)x + b, and we can just remove the parentheses. Since it needs to pass through (5, 4) and it decreases by 1/4x, we plug 4 in for the y value of the equation and 5 in for the x value. This gives you 4 = -1/4(5) + b. -1/4(5) = -1.25, and 4 - (-1.25) = 5.25, which is your value for b. Your final equation should be y = -1/4x + 5.25.
Question two: Parallel lines keep the same slope, so you don't have to do much work to this question. We keep the equation -2x, and again we are just plugging in the coordinate point to our equation. You should get 1 = -2(5) + b, which simplifies to 1 = -10 + b. 1 - (-10) = 11, which is your value for b. You should end up with y = -2x + 11.
Question three: Remember that if there is nothing you can do inside of the parentheses and there are no exponents, you expand whatever you can, which just means to multiply the number right outside of the parentheses by the numbers inside, which in this case would be 5(x + 1). Once you've expanded you should get an equation that looks like this: -4x - 1 + 5x + 5 = -3x - 3. First you collect like terms, which should leave you with x + 4 = -3x - 3. Now we move the variable to one side, and I personally always move negative variables because it is easier to work with. Once you move -3x, you should be left with 4x + 4 = -3. Now just move the constant to the other side and you should get 4x = -7. All that is left for this problem is to divide by 4, so you should get x = -7/4. To check just plug -7/4 back into the original equation, - 4x - 1 + 5(x + 5) = -3x - 3, and see if it is true. Once you substitute -7/4 for every x value and multiply everything, you should see that you are left with a false statement, meaning the original statement is false.
Question four: Since the x value is based on movement left to right, we know that the set of coordinate points with the lowest x value will come first. We just subtract the two coordinate points from each other to get the slope. (-8, 6) - (7, 4). You should end up with -15, 2. But, remember that to write slope it is y/x, so you should end up with 2/-15x
Question five: Since we know that the format for slope is y = mx + b, that is what we need the equation to look like before we solve it. We take the original equation, 5x - 2y + 5 = 0, and when you look at it you should realize that the 5x and 5 need to be moved to get it into slope format. Once you subtract 5x and 5 from both sides, you should be left with -2y = -5x - 5. Now you just divide by -2, and you should be left with y = 2.5x + 2.5
Sorry for going into so much detail, but I tried my best to explain what was going on since you said that you were very lost. Hopefully the explanations help you with future problems also. Best of luck on your class!