Math 10
Unit 6: Linear Functions (Day 4)
Name:
Slope-Point Form
Lesson focus: Relate the graph of a line to its equation in Slope-Point form.
By the end of today you will be able to:
1. Graph a line given its equation in Slope-Point form.
2. Write an equation in Slope-Point form.
3. Write an equation of a line that is parallel to a given line.
How to graph a line when given its equation in Slope-Point form
3
Ex1). Write the slope and the coordinates of a point on the line 𝑦 + 3 = − 4 (𝑥 − 2)
Then graph the line.
Compare the given equation with the equation in slope-point form.
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
slope = m
coordinates = (x1, y1)
3
𝑦 + 3 = − 4 (𝑥 − 2)
slope =
coordinates = (
, )
The line passes through point P(
) and has slope
Ex2) Write the slope and coordinates of a point on the
line 𝑦 + 1 = 3(𝑥 − 2). Then graph the line.
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
𝑦 + 1 = 3(𝑥 − 2)
slope = m
coordinates = (x1, y1)
slope =
coordinates = (
, )
How to Write an equation in Slope-Point form
Ex3). Write an equation for this line in Slope-Point form. Then in Slope-intercept form.
Identify the coordinates of two points on the line, then
calculate the slope.
Two points are:
To calculate slope, m, use:
𝑟𝑖𝑠𝑒
m = 𝑟𝑢𝑛
m=
Equation in Slope-Point form:
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
*substitute slope and
coordinates in
𝑦−
=
(𝑥−
)
Equation in Slope-Intercept form:
Use the Slope-Point form equation; expand, simplify and solve for y
A line can be represented by
many slope-point equations
but only one slope-intercept
equation
How to write an equation of a line that is parallel to a given line
Ex4). Write an equation in Slope-Point form for the line that passes through A(4, 3) and is
1
parallel to the line 𝑦 = − 2 𝑥 + 2
Slope =
*Remember parallel lines have the same slope
The required line passes through A(4, 3). Use the slope-point form of the equation.
1
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
substitute x1 = 4
y1 = 3
and m = − 2
Assignment: P. 372 #4-12,14,18,19,22-25,(27)