Answer Key for California State Standards: Algebra I
|7.0: Students verify that a point lies on a line, given an
equation of the line. Students
are able to derive linear equations by using the point-slope formula.
b. A line has a slope of
and passes through the point (5, 8).
What is the equation for the line?
The equation of the line must be of the form y = mx + b. The slope
given. Therefore, . To find the y intercept b , substitute the
coordinates of the point (5,8) for x and y in the equation . This gives:
This result may also be obtained by using the
point-slope formula for a
|8.0: Students understand the concepts of parallel lines
and perpendicular lines and how
those slopes are related. Students are able to find the equation of a line perpendicular
to a given line that passes through a given point.
a. A line is parallel to the line for the equation:
. What is the slope of the parallel line?
may be rewritten as y = x - 18,
which has slope 1.
Any line parallel to this one must have the same slope, 1.
b. What is the slope of a line perpendicular to the line
equation 3y = 7 - 6x ?
3y = 7 - 6x may be rewritten as . The
slope m of any line
perpendicular to this one must satisfy m(-2) = -1. Therefore
c. What is the equation of a line passing through the
point ( 7, 4 ) and
perpendicular to the line having the equation 3x - 4y - 12 = 0?
The equation 3x - 4y - 12 = 0 may be rewritten as
. The slope of this line
is . The slope m of any line perpendicular to this one must satisfy .
Therefore . So the equation of any perpendicular line must be of the form
. Since the graph of the line contains the point (7,4), it is also true that
So the answer is
. This answer may also be obtained by
|9.0: Students solve a system of two linear equations in
two variables algebraically and
are able to interpret the answer graphically. Students are able to solve a system of two
linear inequalities in two variables and to sketch the solution sets.
a. Solve for the numbers x and y from the equations 2x - y = 1 and 3x - 2y = -1
There are other ways to solve this problem. One
can use one of the
3x - 2(2x - 1) = -1
b. Graph the equations 2x - y = 1 and 3x - 2y = -1 and
circle the portion
of the graph which corresponds to the solution to the above
problem on your graph.
c. Graph the solution to the linear inequalities
2x - y > 1 and 3x - 2y < -1
|10.0: Students add, subtract , multiply, and divide
monomials and polynomials . Students
solve multistep problems, including word problems, by using these techniques.
b. Let P = 2x2 + 3x - 1 and Q = -3x2 + 4x - 1
1. Calculate P + Q and collect like terms.
2. Calculate P - Q and collect like terms.
c. Calculate the product ( x2 - 1 ) ( 2x2 - x - 3 ) and collect like terms.
d. The area of a rectangle is 16. The length of the
and the width is . What is x?
A = length times width