Student Help
EXAMPLE
STUDY TIP
In standard form, a
linear equation can be
written in different
ways. For instance,
another way to write
the equation in Step 6
of Example 2 is
2x y 5.
2
Write an Equation in Standard Form
Write in standard form an equation of the line passing through (4, 3) with a
slope of 2. Use integer coefficients.
Solution
Write the point-slope form.
y y1 m(x x1)
Substitute 2 for m, 4 for x1, and 3 for y1.
y 3 2[x (4)]
Simplify the equation.
y 3 2(x 4)
Use the distributive property.
y 3 2x 8
y 2x 5
Add 3 to each side. (Slope-intercept form)
2x y 5
Add 2x to each side. (Standard form)
Write an Equation in Standard Form
4. Write in standard form an equation of the line passing through (3, 5) with a
slope of 3. Use integer coefficients.
Student Help
EXAMPLE
STUDY TIP
Example 3 uses slopeintercept form (instead
of point-slope form)
because the second
point shows that the
y-intercept is 3.
3
Write an Equation in Standard Form
A line intersects the axes at (4, 0) and (0, 3). Write an equation of the line in
standard form. Use integer coefficients.
Solution
Find the slope. Use (x1, y1) (4, 0) and (x2, y2) (0, 3).
y y
x2 x1
30
04
3
4
2
1 m
Write an equation of the line, using slope-intercept form.
y mx b
Write slope-intercept form.
3
4
3
4
y x 3
冉 34
Substitute for m and 3 for b.
冊
4y 4 x 3
Multiply each side by 4.
4y 3x 12
Use distributive property.
3x 4y 12
ANSWER 䊳
Add 3x to each side.
The equation 3x 4y 12 is in standard form.
Write an Equation in Standard Form
5. Write in standard form an equation of the line that intersects the axes at (2, 0)
and (0, 5). Use integer coefficients.
292
Chapter 5
Writing Linear Equations