The Girl Scout troop has a budget of 50 to set up a take sal

The Girl Scout troop has a budget of $50 to set up a take sale at the farmer\'s market. It costs $10 to rent a table and each cupcake costs 25 cents to make. How many cupeakes can they make in their budget? [Be sure to define your variable(s), write out the equation, and the solve the equation.] Find an equation of the line with the given y-intercept and slope m. y-intercept = -3 and m^- -7 Determine whether the pair of lines is parallel, perpendicula, or neither. x - 3y = 4 and y = 1 - 3x Find an equation that satisfies the given conditions. Through (6,8) and perpendicular to y = 2x - 3 In the following problem, assume that the data can be modeled by a straight line. Use two points to find such a line and then answer the question. MUST SHOW EQUATION OF LINE OR NO CREDIT. The Consumer Price Index(CPI), which measure the cost of a typical package of consumer goods, stood at 130 in 1990 and 170 in 2000. Let x=0 correspond to 1990 and estimate the CP in 1995 and 2003.

Solution

12. The budget of the girls scout troop is $ 50 out of which, the cost of renting a table is $ 10, so that the remaining amout is $ 40. Let x be the nuber of cupcakes that the girls scout troop can make . Since the cost of making a cupcake is 25 cents or. $ 0.25, the cost of making x cupcakes is 0.25x . Since $ 40 are available to make cupcakes, we have 0.25x = 40 or, on multiplying both the sides by 4, x = 40* 4 = 160. Thus the girls scout troop can make 160 cupcakes within the available budget.

13 The equation of a line in the slope intercept form is y = mx + c where m is the slope and c is the y-intercept. Here, m = -7 and c = -3. Therefore, the equation of the required line is y = - 7x - 3.

14.The given lines are x - 3y = 4 and y = 1 - 3x If . x - 3y = 4, then 3y = x - 4 or, y = 1/3 x - 4/3...(1) The other line is y = - 3x + 1… (2)

If we visualize a line with positive slope as an increasing line, then the perpendicular line must have negative slope because it will be a decreasing line. So, the slopes of the lines with perpendicular slopes have opposite signs. The other characteristic with perpendicular slopes is that their values are reciprocals. In the given exercise, the slopes of the two lines are 1/3 and – 3 which have opposite signs. Also, 1/3 is the reciprocal of 3. Therefore, the given lines are perpendicular to each other.

15. Let the equation of the given line be y = m x +c. Since this line passes through the point (6, 8), we have 8 = 6m + c . Also, since this line is perpendicular to the line y = 2x -3, its slope is – ½. Therefore m = - ½. Then , we have 8 = 6 ( -1/2) + c or, 8 = - 3 + c ,    so that c = 8 + 3 = 11. Then the equation of the required line is y = ( - ½) x + 11