write linear equations in standard form you will write equations in standard form how do you write...
TRANSCRIPT
Write Linear Equations in Standard Form
• You will write equations in standard form
• How do you write equations in standard form?
You will learn how to answer this question by rewriting equations.
Warm-Up Exercises
To write another equivalent equation, multiply each side by 0.5.
4x – 12y = 8
To write one equivalent equation, multiply each side by 2.
SOLUTION
Write two equations in standard form that are equivalent to 2x – 6y = 4.
EXAMPLE 1 Write equivalent equations in standard form
x – 3y = 2
Warm-Up Exercises
SOLUTION
y = mx +b
Calculate the slope.STEP 1
EXAMPLE 2 Write an equation from a graph
–3m =1 – (–2)
1 – 2=
3–1 =
Write an equation in slope-intercept form. Use (1, 1).
1 = –3( 1) + b
Write an equation in standard form of the line shown.
STEP 2
b= 4
y= -3x + 4
Warm-Up Exercises
Rewrite the equation in standard form.
EXAMPLE 2 Write an equation from a graph
3x + y = 4
STEP 3
y= -3x + 4
Warm-Up ExercisesEXAMPLE 1GUIDED PRACTICE for Examples 1 and 2
Write two equations in standard form that are equivalent to x – y = 3.
1.
2x – 2y = 6, 3x – 3y = 9ANSWER
Warm-Up ExercisesEXAMPLE 2 Write an equation from a graphGUIDED PRACTICE for Examples 1 and 2
Write an equation in standard form of the line through (3, –1) and (2, –3).
2.
–2x + y = –7ANSWER
Warm-Up Exercises
SOLUTION
EXAMPLE 3 Write an equation of a line
Write an equation of the specified line.
The y-coordinate of the given point on the blue line is –4. This means that all points on the line have a y-coordinate of –4. An equation of the line is y = –4.
a.
The x-coordinate of the given point on the red line is 4. This means that all points on the line have an x-coordinate of 4. An equation of the line is x = 4.
b.
Blue linea. Red lineb.
Warm-Up Exercises
Simplify.
Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A.
STEP 1
SOLUTION
EXAMPLE 4
Find the missing coefficient in the equation of the line shown. Write the completed equation.
Ax + 3y = 2A(–1) + 3(0) = 2
–A = 2A = –2
Write equation.
Substitute –1 for x and 0 for y.
Divide by –1.
EXAMPLE 3EXAMPLE 4Complete an equation in standard form
Warm-Up ExercisesEXAMPLE 4Complete an equation in standard form
Complete the equation.
–2x + 3y = 2 Substitute –2 for A.
STEP 2
Warm-Up Exercises
Write equations of the horizontal and vertical lines that pass through the given point.
GUIDED PRACTICE for Examples 3 and 4
3. (–8, –9)
y = –9, x = –8ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
4. (13, –5)
y = –5, x = 13ANSWER
Write equations of the horizontal and vertical lines that pass through the given point.
Warm-Up ExercisesEXAMPLE 4Complete an equation in standard form
Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.
EXAMPLE 3 Write an equation of a lineGUIDED PRACTICE for Examples 3 and 4
5. –4x + By = 7, (–1, 1)
ANSWER 3; –4x + 3y = 7
Warm-Up ExercisesEXAMPLE 4Complete an equation in standard formEXAMPLE 3 Write an equation of a lineGUIDED PRACTICE for Examples 3 and 4
6. Ax + y = –3, (2, 11)
Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.
ANSWER –7; –7x +y = –3
Warm-Up Exercises
LIBRARY
EXAMPLE 5
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.
b. Graph the equation from part (a).
c. List several possible combinations.
Solve a multi-step problem
Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill.
a.
Warm-Up Exercises
SOLUTION
a. Write a verbal model. Then write an equation.
Because your class could fill 15 small vans and 2 large vans, use (15, 2) as the s- and l-values to substitute in the equation 8s + 12l = p to find the value of p.
8(15) + 12(2) = p Substitute 15 for s and 2 for l.144 = p Simplify.
Substitute 144 for p in the equation 8s + 12l = p.
EXAMPLE 5 Solve a multi-step problem
8 s l p12+ =
Warm-Up Exercises
Substitute 0 for s.8(0) + 12l = 144
l = 12
Substitute 0 for l.
s = 188s + 12(0) = 144
ANSWER
The equation 8s + 12l = 144 models the possible combinations.
b. Find the intercepts of the graph.
EXAMPLE 5 Solve a multi-step problem
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
Plot the points (0, 12) and (18, 0). Connect them with a line segment. For this problem only nonnegative whole-number values of s and l make sense.
The graph passes through (0, 12), (6, 8), (12, 4), and (18, 0). So, four possible combinations are 0 small and 12 large, 6 small and 8 large, 12 small and 4 large, 18 small and 0 large.
c.
Warm-Up ExercisesDaily Homework Quiz
Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the two given points.
ANSWER 2x + y = –4
1.
(1, –6), m = –2
2. (–4, –3), (2, 9)
ANSWER –2x + y = 5
Warm-Up ExercisesDaily Homework Quiz
ANSWER
8p + 6c = 96; 16 h kayak and 0 h paddleboat; 12 h paddleboat and 0 h kayak; 6 h paddleboat and 8 h kayak.
3.
You have $96 to spend on campground activities. You can rent a paddleboat for $8 per hour and a kayak for $6 per hour. Write an equation in standard form that models the possible hourly combinations of activities you can afford. List three possible combinations.
• You will write equations in standard form
• How do you write equations in standard form?
Ax + By = C is the standard form of an equation where A, B, and C are real numbers, and A and B are not both 0.
Use the slope formula to find the slope. Write the equation in y = mx + b form. Collect the variable terms on one side of the equation and constants on the other to rewrite the equation in standard form.