The coordinate plane below represents a community. Points A through F are houses in the community.
1 answer:
A1) One possible set of inequalities is
x +y > 2
y -x < 4
A2) The lines are graphed as though the inequality were an equal sign. Since the inequality does not include the "or equal to" case, the lines are drawn dashed. In each case, the area to the right of the line is shaded.
B) Points A and B are solutions to the system if they are in the doubly-shaded region (which they are). In the graph here, that region is darker orange. (For this purpose, you need to ignore the green region, which overlaps part of the solution space.
C) The houses Billy is interested in are found by graphing the inequality and identifying the houses in its solution space. (Those houses are B and C.) Alternatively, you can evaluate the inequality for each of the house coordinates and see which ones give "true."
x +y > 2
y -x < 4
A2) The lines are graphed as though the inequality were an equal sign. Since the inequality does not include the "or equal to" case, the lines are drawn dashed. In each case, the area to the right of the line is shaded.
B) Points A and B are solutions to the system if they are in the doubly-shaded region (which they are). In the graph here, that region is darker orange. (For this purpose, you need to ignore the green region, which overlaps part of the solution space.
C) The houses Billy is interested in are found by graphing the inequality and identifying the houses in its solution space. (Those houses are B and C.) Alternatively, you can evaluate the inequality for each of the house coordinates and see which ones give "true."
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Part 1
Let:
y be the total cost
x be the number of tickets
a be fair admission
Since the fair charges $1.25 per ticket, the equation of the line would look like:
y = 1.25x + a
Since Johnny spent $43.75 and bought 25 tickets, we find a by replacing y with 43.75 and x with 25:
43.75 = 1.25×25 + a
Now solve for a
43.75 = 31.25 + a
43.75 - 31.25 = a
a = 12.50
Going back to the first equation:
y = 1.25x + 12.50
Part 2:
a) Let (9,8) be (x1,y1) and (4,-12) be (x2,y2)
The formula for slope is:
b) For the point-slope equation, I'll use (9,8)
Using the formula:
c) For the slope-intercept form, we solve for y in the point-slope formula:
Let:
y be the total cost
x be the number of tickets
a be fair admission
Since the fair charges $1.25 per ticket, the equation of the line would look like:
y = 1.25x + a
Since Johnny spent $43.75 and bought 25 tickets, we find a by replacing y with 43.75 and x with 25:
43.75 = 1.25×25 + a
Now solve for a
43.75 = 31.25 + a
43.75 - 31.25 = a
a = 12.50
Going back to the first equation:
y = 1.25x + 12.50
Part 2:
a) Let (9,8) be (x1,y1) and (4,-12) be (x2,y2)
The formula for slope is:
b) For the point-slope equation, I'll use (9,8)
Using the formula:
c) For the slope-intercept form, we solve for y in the point-slope formula: