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Linear Equations
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Systems of Equations
Word Problems
100
In Slope-Intercept Form, write the equation of the line with a slope of 4 that passes through (2,10).
y = 4x + 2
100
Find a value of k so that (3,1) satisfies the equation x + 2y = k.
k = 5
100
If f(x) = 4x + 7, find f(-3)
f(-3) = -5
100
Solve the following System of Equations: x + y = -2 and 2x - y = 11
(3,-5)
100
Solve Using a System of Equations You receive $80 for your birthday in $5 and $10 bills. If you have a total of 13 bills, how many of each type do you have?
10 $5 Bills and 3 $10 Bills.
200
In Slope-Intercept Form, write the equation of the line that passes through (0,6) and (2,9).
y = 3/2 x + 6
200
Find a value of k so that the line containing (4,3) and (k,6) has a slope of 6.
k = 4.5
200
If f(x) = 2x + 8, find the value of x so that f(x) = 9
x = 0.5
200
Solve the following System of Equations: x = 16 - 2y and 3x + 4y = 32
(0,8)
200
Solve using a System of Equations When riding with the current, a boat can make a 300 mile trip in 6 hours. Riding against the same current, the return trip would take 10 hours. Find the Boat Speed and the Current Speed.
Boat Speed: 40 mph Current Speed: 10 mph
300
In Slope-Intercept Form, write the equation of the line that passes through (2,1) and (-3,-1).
y = 2/5 x + 1/5
300
Find a value of k so that the line 2x + ky = 9 has a y-intercept of 1.
k = 9
300
If f(x) = 2x - 7 and g(x) = (x+2)(x-3), find f(g(1)).
f(g(1)) = -19
300
Solve the following System of Equations: 3x + 5y = 23 and 2x + 7y = 30
(1,4)
300
Solve using a System of Equations If Mr. Calnan sold all of his Southbridge shirts for $10 and all of his Southbridge jackets for $25, he would make $130. If he sold all of the items for $20, he would make $200. How many of each item does he have?
8 shirts and 2 jackets.
400
In Slope-Intercept Form, write the equation of the line that is parallel to the line y = 3x +8 and passes through (-2,6).
y = 3x + 12
400
Find a value of k so that y = 3x + 6 is perpendicular to the line 5x - ky = 10.
k = -15
400
Identify the domain of f(x) = 3/(2x+5).
All Real Numbers except -5/2.
400
Solve the following System of Equations: 8x + 4y = 11 and y = -2x +3
No Solution
400
Solve using a System of Equations A financial planner wants to invest $8000, some in stocks earning 15% interest, and the rest in bonds earning 6% interest. How much should be invested in each account to earn $1020 in interest?
Stocks: $6000 Bonds: $2000
500
In Slope-Intercept Form, write the equation of the line perpendicular to the line y = 1/2 x + 8 that passes through (-8, 12).
y = -2x - 4
500
Find a value of k so that (k+2)x + (3k+1)y = 8 is perpendicular to the line x = 8.
k = -2
500
Identify the domain of g(x) = 4/sqrt(3x-7)
x > 7/3
500
Solve the following System of Equations: 2x - 6y = 15 and -5x + 15y = -37.5
Infinitely Many Solutions
500
Solve using a System of Equations The sum of the measures of the base angles of an isosceles triangle is 30 degrees less than half of the vertex angle's measure. Find the three angle measures.
The angles of the triangle are 20 degrees, 20 degrees, and 140 degrees.