Download Les. 4-5 Writing Equations in Point

Learning Goals
Derive linear equations by using Point-Slope formula.
Write a linear equations in different forms.
Writing Linear Equations in Point-Slope Form
Write an equation in point-slope form for the line with the
given slope that passes through the given point.
A.
B.
C.
Try This!
Write an equation in point-slope form for the line with the
given slope that contains the given point.
a.
b. Horizontal Line; (3, –4)
y – (–4) = 0(x – 3)
y + 4 = 0(x – 3)
y+4=0
Writing Linear Equations in Slope-Intercept Form
Write an equation in slope-intercept form for the line with
slope 3 that contains (–1, 4).
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
y – 4 = 3[x – (–1)]
Step 2 Write the equation in slope-intercept form by solving
for y.
y – 4 = 3(x + 1)
y – 4 = 3x + 3
+4
+4
y = 3x + 7
Rewrite subtraction of negative numbers as
addition.
Distribute 3 on the right side.
Add 4 to both sides.
Try This!
Write an equation in slope-intercept form for the line with
slope that contains (–3, 1).
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
Step 2 Write the equation in slope-intercept form by solving for y.
Rewrite subtraction of negative
numbers as addition.
Distribute
+1
+1
on the right side.
Add 1 to both sides.
Using Two Points to Write an Equation
Write an equation in slope-intercept form for the line
through the two points.
(2, –3) and (4, 1)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the
point-slope form.
y – y1 = m(x – x1)
Choose (2, –3). (But you can
y – (–3) = 2(x – 2)
Choose either point.)
Step 3 Write the equation in slope-intercept form.
y + 3 = 2(x – 2)
y + 3 = 2x – 4
–3
–3
y = 2x – 7
Using Two Points to Write an Equation
Write an equation in slope-intercept form for the line
through the two points.
(0, 1) and (–2, 9)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the
point-slope form.
y – y1 = m(x – x1)
Choose (0, 1).
y – 1 = –4(x – 0)
Step 3 Write the equation in slope-intercept form.
y – 1 = –4(x – 0)
y – 1 = –4x
+1
+1
y = –4x + 1
Try This!
Write an equation in slope-intercept form for the line through the
two points.
(1, –2) and (3, 10)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the
point-slope form.
y – y1 = m(x – x1)
Choose (1, –2).
y – (–2) = 6(x – 1)
y + 2 = 6(x – 1)
Step 3 Write the equation in slope-intercept form.
y + 2 = 6(x – 1)
y + 2 = 6x – 6
–2
–2
y = 6x – 8
Try This!
Write an equation in slope-intercept form for the line through
the two points.
(6, 3) and (0, –1)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the
point-slope form.
y – y1 = m(x – x1)
Choose (6, 3).
Step 3 Write the equation in slope-intercept form.
+3
+3
Standard Form of a Linear Equation
Notice that when a linear equation is written in
standard form
• x and y both have exponents of 1.
• x and y are not multiplied together.
• x and y do not appear in denominators, exponents, or
radical signs.
• A, B, or C cannot be a fraction.
Rewriting Equations in Standard Form
Rewrite the equation in standard form.
Multiply both sides by 3, to clear the
fraction.
3y = x – 6
–x -x____
–x + 3y = –6
Write the equation in standard form.
Rewriting Equations in Standard Form
Rewrite the equation in standard form.
1
1
12( x )  12(2  y )
4
3
3x = 24 – 4y
+4y
+4y
4y + 3x = 24
Multiply both sides by 12, to clear the
fraction.
Write the equation in standard form.
Application
The school sells pens for $2.00 and notebooks for
$3.00. The equation 2x + 3y = 60 describes the number
of pens x and notebooks y that you can buy for $60.
What does each intercept represent?
x-intercept: 30. This is the
number of pens that can be
purchased if no notebooks are
purchased.
y-intercept: 20. This is the
number of notebooks that can
be purchased if no pens are
purchased.