1. Standard Form Examples 3x + y = 5 -2x + y = 10 x – y = 6
ALGEBRA 1 LESSON 6-3 )
Examples
3x + y = 5 -2x + y = x – y = 6
20x + 4y = 8 9x - 3y = 1 2x + 5y = 4
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2. Standard Form Find the x- and y-intercepts of 2x + 5y = 6.
ALGEBRA 1 LESSON 6-3
Find the x- and y-intercepts of 2x + 5y = 6.
Step 1  To find the x-intercept, substitute 0 for y and
solve for x.
2x + 5y = x + 5(0) = x = x = 3
The x-intercept is 3.
Step 2  To find the y-intercept,
substitute 0 for x and
solve for y.
2x + 5y = 6
2(0) + 5y = 6
5y = 6
y =
The y-intercept is . 6 5
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3. Standard Form Graph 3x + 5y = 15 using intercepts.
ALGEBRA 1 LESSON 6-3
Graph 3x + 5y = 15 using intercepts.
Step 1  Find the intercepts.
3x + 5y = 15
3x + 5(0) = 15 Substitute 0 for y.
3x = 15 Solve for x.
x = 5
3(0) + 5y = 15 Substitute 0 for x.
5y = 15 Solve for y.
y = 3
Step 2  Plot (5, 0) and (0, 3).
Draw a line through the points.
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4. Standard Form a. Graph y = 4 b. Graph x = –3.
ALGEBRA 1 LESSON 6-3
a. Graph y = 4
b. Graph x = –3.
0 • x + 1 • y = 4 Write in standard form.
For all values of x, y = 4.
1 • x + 0 • y = –3 Write in standard form.
For all values of y, x = –3.
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5. Standard Form Write y = x + 6 in standard form using integers. 2
ALGEBRA 1 LESSON 6-3
Write y = x + 6 in standard form using integers. 2 3
y = x + 6 2 3
3y = 3( x + 6 ) Multiply each side by 3.
3y = 2x Use the Distributive Property.
–2x + 3y = Subtract 2x from each side.
The equation in standard form is –2x + 3y = 18.
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6. Standard Form
ALGEBRA 1 LESSON 6-3
Write an equation in standard form to find the number of hours you would need to work at each job to make a total of $130.
Define:  Let = the hours mowing lawns.
Let = the hours delivering newspapers. x y
Amount Paid per hour
Job
Mowing
lawns
$12
Delivering
newspapers
Relate: $12 per h   plus $5 per h equals   $130
mowing delivering $5
Write:  = x y
The equation standard form is 12x + 5y = 130.
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7. Standard Form Find each x- and y-intercepts of each equation.
ALGEBRA 1 LESSON 6-3
Find each x- and y-intercepts of each equation.
1. 3x + y = –4x – 3y = 9
3. Graph 2x – y = 6 using x- and y-intercepts.
For each equation, tell whether its graph is horizontal or vertical.
4. y = x = –8
6. Write y = x – 3 in standard form using integers.
x = – , y = –3 9 4
x = 4, y = 12
horizontal
vertical 5 2
–5x + 2y = –6 or 5x – 2y = 6
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