1. Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problems SPI 21D: determine the slope given a graph of a linear equations (VS) SPI 21E: determine the slope when given the coordinates of 2 points
Objectives:
Graph lines given their equations
Write equations of lines
Linear Equation:
equation of a line
all points on the line are a solution to the equation
Forms of Linear Equations:
Slope-Intercept
Standard Form
Point-slope Form

2. Review Slope Formula Slope or Rate of Change
Slope = change in y
change in x
Slope = y2 – y1
x2 – x1
One pair of
coordinates
The other pair
of coordinates
Using Slope to graph an equation
From known point:
Top number is rise: Move up (+) or down (-)
Bottom number: Move right

3. Review Slope Intercept Form
y = mx + b Y I II
III IV
f(x)
slope
y-intercept
Graph y = 3 x + 2 4 X
1. Plot y-intercept
2. From known point, plot
slope. (Rise over run)
3. Connect the 2 points
with a line.

4. Practice II I III IV Slope Intercept Form Graph y = - 1 x – 2 2
1. Plot y-intercept X
2. From known point, plot
slope.
3. Connect the 2 points
with a line.

5. Review: Standard Form of a Linear Equation (Graph using x and y intercepts)
Ax + By = C
Graph 6x + 3y = 12 Y
1. Find x intercept:
Substitute 0 for y; solve for x I II
III IV
6x + 3(0) = 12
6x = 12
x = 2
(0, 4)
(2, 0) X
2. Find y intercept:
Substitute 0 for x; solve for y
6(0) + 3y = 12
3y = 12
y = 4
3. Plot x and y intercepts: (2, 0) and (0, 4)
Connect points with line

6. Practice
Graph a Linear Equation in Standard Form (Graph using x and y intercepts)
Ax + By = C
Graph -2x + 4y = - 8 Y
1. Find x intercept:
Substitute 0 for y; solve for x I II
III IV
-2x + 4(0) = - 8
-2x = - 8
x = 4
(4, 0) X
(0, -2)
2. Find y intercept:
Substitute 0 for x; solve for y
-2(0) + 4y = - 8
4y = - 8
y = - 2
3. Plot x and y intercepts: (4, 0) and (0, -2)
Connect points with line

7. Alternate Method to Graph Equation in Standard Form Change Equation to Slope-Intercept Form
Ax + By = C
y = mx + b
Graph -2x + 4y = - 8 Y I II
III IV
1. Use Properties of Equality to
Solve equation in terms of y.
-2x + 4y = - 8
+2x = x
4y = 2x – 8
y = 1 x – 2 2
(2, -1) X
(0, -2)
2. Plot the y-intercept: -2
Plot the slope: ½
3. Plot x and y intercepts: (4, 0) and (0, 3)
Connect points with line

8. Change Standard Form to Slope- Intercept Form and Graph
Practice
Change Standard Form to Slope- Intercept Form and Graph
Graph 6x + 3y = 12 Y
1. Use properties of equality to
solve the equation in terms of y. I II
III IV
6x + 3y = 12
-6x = 12 – 6x
3y = -6x + 12
y = -2x + 4
(0, 4)
(1, 2) X
2. Plot the y-intercept: 4
Plot the slope: - 2

9. Review: Point-slope Form of a Linear Equation
Write an equation of a line given two points. A(-2, 3) and B(1, -1).
y – y1 = m(x – x1)
(x, y)
(x1, y1)
1. Find the slope.
2 Set of coordinates
m = y2 – y1 = 3 – (-1) = 4
x2 – x (-2) –
Write an equation of the line thru point P(-1, 4) with slope 3.
Substitute known values into the equation.
2. Select one of the points and substitute values into equation. Pick (-2, 3).
y – (4) = 3 (x – (-1)) Sub.
y – 4 = 3 (x + 1) Simplify
y – y1 = m(x – x1)
y – y1 = m(x – x1)
y = - 4/3(x – (-2))
y – 3 = - 4/3(x + 2)

10. II I III IV Equations of Horizontal and Vertical Lines
Graph a Horizontal Linear Equation Y
Graph the equation y = 3. I II
III IV
1. Plot the point (0, 3)
2. Draw a horizontal line.
(0, 3) X
For all values of x in the graph of y = 3, what is the value of y?

11. Practice II I III IV Equations of Horizontal and Vertical Lines
Graph a Vertical Linear Equation Y
Graph the equation x = 4. I II
III IV
1. Plot the point (4, 0)
2. Draw a vertical line.
(4, 0) X
For all values of y in the graph of x = 4, what is the value of x?