Download 5.4 Write Linear Equations in Standard Form Warm-up

5.4 Write Linear Equations in Standard Form
Warm-up:
1. Write an equation in point-slope form of the line that passes through (6,-4) and has a slope
of 2.
2. Write an equation in point-slope form of the line that passes through (-5, 3) and has a slope
of ½ .
3. Write two equations in point-slope form of the line that passes through (-1,-6) and (3,10).
4. Rewrite each of the two point-slope equations in question 3 in slope-intercept form.
5. A travel company offers guided rafting trips for $875 for the first three days and $235 for
each additional day. Write an equation that gives the total cost (in dollars) of a rafting trip
as a function of the length of the trip.
6. Using your equation from #5, find the cost for a 7-day trip.
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Goal • Write equations in standard form.
Example 1 Write equivalent equations in standard form
Write three equations in standard form that are equivalent to 4x + 2y = 12.
To write one equivalent equation, multiply each side by_______: __________________
To write another equivalent equation, multiply each side by_______: __________________
To write another equivalent equation, divide each side by_______: __________________
Write two equations in standard form that are equivalent to −12x + 6y= −9
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2.
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Checkpoint Complete the following exercises.
Write two equations in standard form that are equivalent to 6x − 4y = 6
Example 2 Write an equation from a graph
Write an equation in standard form of the line shown.
Step 1 Calculate the slope.
y −y
m= 2 1
x2 − x
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All linear equations can be written in standard form, Ax +By =c
Step 2 Write an equation in point-slope form. Use the point (2, 4).
Step 3 Rewrite the equation in standard form.
3.
Checkpoint Complete the following exercise.
Write an equation in standard form of the line through (3, −1) and (2, −4).
Example 3 Write an equation of a line
Write an equation of the specified line.
a. Line A
The x-coordinate of the given point on Line A is ___. This means
that all points on the line have an x-coordinate of___. An equation
of the line is ________________.
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points on the line have a y-coordinate of____. An equation of the line is __________.
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b. Line B
The y-coordinate of the given point on Line B is____. This means that all
Example 4 Complete an equation in standard form
Find the missing coefficient in the equation of the line shown.
Write the completed equation.
Step 1 Find the value of A. Substitute the coordinates of the given point
for x and y in the equation.
Ax + 5y = −3
Write equation.
A(___) + 5(___) = −3
Substitute ____for x and___for y.
___A +___= −3
Simplify.
___A =____
Subtract ____ from each side.
A = ____
Divide by___.
Step 2 Complete the equation.
____x + 5y = −3
4.
Substitute ____for A.
Checkpoint Complete the following exercises.
Write equations of the horizontal and vertical lines that pass through (−10, 5).
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5.
Find the missing coefficient in the equation of the line that passes through (−2, 2). Write the
completed equation.
6x + By = 4
Example 5 – Solve a Multi-Step Problem
Library: Your class is taking a trip to the public library. You can travel in small and large vans. A
small van holds 8 people and a large van holds 12 people. Your class could fill 15 small vans and 2
large vans.
a. Write an equation in standard form that models the possible combinations of small vans and
large vans that your class could fill.
b. Graph the equation from part (a).
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c. List several possible combinations.