Download Algebra Unit V, Section 5.5

Point-Slope Form of an
Equation (5.5)
Where does the Point-Slope form come from?
Example 1: Writing Linear Equations in
Point-Slope Form
Write an equation in point-slope form for the line with the
given slope that contains the given point.
A.
B.
y -3 = -4(x)
C.
You try it: Example 1
Write an equation in point-slope form for the line with the
given slope that contains the given point.
a.
b. slope = 0; (3, –4)
y – (–4) = 0(x – 3)
y + 4 = 0(x – 3)
y+4=0
y = -4
Example 2: 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.
Rewrite subtraction of negative
y – 4 = 3(x + 1)
numbers as addition.
y – 4 = 3x + 3
Distribute 3 on the right side.
+4
+4
Add 4 to both sides.
y = 3x + 7
Example 3: 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)
y – (–3) = 2(x – 2)
Choose (2, –3).
Additional Example 3 Continued
We now have the following:
y – (–3) = 2(x – 2)
Step 3 Write the equation in slope-intercept form.
y + 3 = 2(x – 2)
y + 3 = 2x – 4
–3
–3
y = 2x – 7
Additional Example 4: 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)
y – 1 = –4(x – 0)
Choose (0, 1).
Additional Example 4 Continued
Write an equation in slope-intercept form for the line
through the two points.
(0, 1) and (–2, 9)
Step 3 Write the equation in slope-intercept form.
y – 1 = –4(x – 0)
y – 1 = –4x
+1
+1
y = –4x + 1
Summary/Review
You have now learned how to write the equation of a line in
three different forms.
A. Slope-Intercept
B. Point-Slope
Ax + By = C
y = mx + b
-Must be solved for
“y”
-Must have values
in place of m and b
C. Standard
-Plug values in
for m, x1 and y1
-The term with the x
must come first
-A, B, and C must be
Integers
-A must be positive
Summary Quiz:
Find the equation of the line that has a slope of
3 and goes through the point (-1, 5) in:
a) Point-Slope Form
y-5 = 3(x+1)
b) Slope-Intercept Form
y = 3x+8
c)
Standard Form
3x – y = -8