Name:
Ms. D’Amato
Date:
Block:
Point-Slope Form and Standard Form
The
(x1, y1) with a slope of m is:
of the equation of a nonvertical line that passes through a given point
y – y1 = m(x – x1)
Write an equation in point-slope form:
1. Write an equation in point-slope form
of a line that passes through the point
(4, -3) and has a slope of 2.
2. Write an equation in point-slope form
of a line that passes through the point (-1, 4)
and has a slope of -2.
Graph an equation in point-slope form:
2
1. Graph the equation y + 2 = (x – 3).
3
2. Graph the equation: 𝑦 − 1 = −(𝑥 − 2)
Use Point-Slope Form to Write an Equation:
Steps:
1. Find the slope of the line.
2. Write the point-slope equation. ( y – y1 = m(x – x1) )
3. Substitute in the slope and ONE of the points of your choice.
a. Write an equation in point-slope form of the line shown.
b. Write an equation in point-slope form of the line that passes through the points (2, 3) and (4, 4).
Recall that the linear equation Ax + By = C is in
, where A, B and C
are real numbers and A and B are not both zero. All linear equations can be written in standard form.
Write an equation in standard form:
Steps:
1. Find the slope of the line.
2. Write the point-slope equation. ( y – y1 = m(x – x1) )
3. Substitute in the slope and ONE of the points of your choice.
4. Distribute.
5. Rewrite the equation in standard form.
Example 1: Write an equation in standard form from a graph.
Example 2: Write an equation in standard form of a line that has a slope of 3 and goes through the point
(3, -6).
Example 3: Write an equation in standard form of the line through (3, -1) and (2, -3).
Write Equations of Horizontal and Vertical Lines:
Zero slope
y=#
Undefined slope
x=#
Example:
y=2
Example:
x=2
HOY VUX
HOY
VUX
Write equations of the horizontal and vertical lines that pass through the given point.
1. (-8, -9)
2. (13, -5)
Vertical Line:
Horizontal Line:
Vertical Line:
Horizontal Line:
Complete an Equation in Standard Form:
Steps:
1. Write the equation.
2. Substitute values in for x and y.
3. Solve for the variable.
4. Substitute your answer in for the variable to write the completed equation.
Find the missing coefficient in the equation of the line that passes through the given point. Write
the completed equation.
1. -4x + By = 7; (-1, 1)
2. Ax + y = -3; (2, 11)
Word Problems: Equations in Standard Form.
1. Your class is taking a trip to the public library. You can travel in small and large vans. A small van holds
8 people and a large van holds 12 people. Your class has a total of 144 people. Write an equation in
standard form that models the possible combinations of small vans and large vans your class could fill.
2. Karen has 2 jobs. She baby-sits and gives music lessons. One weekend she worked a total of 18 hours.
a. Write an equation to represent the hours she spend baby-sitting and giving music lessons.
b. Karen makes $5 per hour baby-sitting and $12 per hour giving music lessons. One weekend she made
$139. Write an equation to represent her earnings.