Sarah saved $12.75 every week for a number of weeks, w. she received an additional $25 during the last week in which she saved money. write and solve an equation to find the number of weeks, w for which sarah had saved money if she has $114.25 now

12.75w + 25 = 114.25

w = 7

Step-by-step explanation:

since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet)  we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.

to find out what w represents, we have to solve for it. solving for w means isolating it on one side. so, what we can do first is subtract 25 from both sides. that would then make the equation:

12.75w = 89.25

now, we have only one step left to isolating w, and that's to get 12.75 on the other side somehow. since we're multiplying 12.75 with w, and we're applying additive inverse properties, meaning the opposite of what is happening to cancel it out on the side it's in, we would divide 12.75 on both sides. in the left, 12.75 would cancel out, and in the right, we would divide 89.25 by 12.75. the quotient is 7.

now there's nothing left to take out to isolate w, so we have:

w = 7

sarah saved up for 7 weeks.

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct