Find the equation of the line that passes through the points(4,-7) and has a slope of 3

In order to solve this problem we can use the Point-Slope Form. Our Given Slope is 3 and our given point is (4,-7) the Point Slope Form Looks something like this y-y(1)=m(x-x1) The y,x are constants while the y1 and x1 is given to you in the point 4=x1 and -7=y1 M is slope and our slope is 3 SO Now We Plug In :) y-(-7)=3(x-4) The negative sign in front of of the (-7) will change that part of the equation to y+7 because two negatives multiplied together gives you a positive number. y+7=3(x-4) Now We can distribute the 3 y+7=3x-12 Lastly we want y by itself so we can have it in slope-intercept form which looks like y=mx+b. So now subtract 7 on each side. y=3x-19

Leo had $44 to spend on six fancy pens. After buying them he had $20. How much did each pen cost?

What information is given to us from the problem: Leo started off with $44 and now he is only left with $20 after purchasing the pens. What are we trying to figure out: How much each pen cost? We would start off by formulating a equation with the given info and for the unknown we will use the variable "p" which represents the price of the pen. *Notice we added a 6 in front of the "p" just because he purchased 6 of these fancy pens. $44-6p=$20 Now we can add "6p" on each side so we can start to separate the variable. $44=6p+20 We can now subtract 20 from each side to get the "6p" on the side alone. 24=6p In order to complete the problem and figure out the price, we have to divide by 6 on each side.If not this is telling us the price of 6 pens and we want to know the price of each one. p=4 In all the pens was $4 each.

Kimberly is 6 years older than John. 6 years ago she was twice as old as he. How old is Kimberly and John now?

Let x=John's age now x+6=Kimberly's age now x-6=John's age 6 years ago (x+6)-6=Kimberly's age 6 years ago Remember Six Years ago she was twice the age of John. Let's Make our Equation: (x+6)-6=2(x-6) Simplify x=2x-12 12=x (Johns's Age now) x+6 is Kimberly's Age Now so 12+6=18 John is 12 years of age Kimberly is 18 years of age