1. Solving & Graphing
Simple Linear Equations
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By:
Elizabeth Eme

2. A linear equation is a first degree polynomial equation
1. Slope-intercept form
– Formula & definition
– Example
– Pop Quiz
2. General form
– Formula & definition
– Example
– Pop Quiz
3. Graphing
– Using T-chart
– Using Slope & y-intercept
– Pop Quiz
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3. Slope – Intercept Form
• y = mx + b [m=slope; b= y-intercept]
• Slope – Intercept form is one way to
express a linear equation. Equations may
begin in slope-intercept form or they may be
solved into slope-intercept form.
• This form allows a student to read the
slope and y-intercept directly from the
equation.
• Slope is the rate of change between points.
The y-intercept is where the line crosses
the y-axis. Next
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4. Slope - Intercept Form
• Original Equation
y + 4 = -7 (x – 1)
• Distribute -7 to (x-1)
y + 4 = -7*x -7*(-1)
y + 4 = -7x + 7
• Subtract 4 from both sides
y +4 – 4 = -7x + 7 – 4
y = -7x + 3
• Slope = -7; y-intercept = 3
Next
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5. Slope – Intercept Form
• Pop Quiz!
– What does the ‘m’ stand for in a linear
equation in the form y = mx + b?
• A) x-intercept
• B) y-intercept
• C) slope
(answers will be given at the conclusion)
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6. General/Standard Form
• ax + by = c
• General or standard form is another way to
express a linear equation. The equation
may begin in this form or be solved into this
form.
• The slope may be determined from this
form by taking the opposite sign of a÷b
(i.e. –a÷b)
• The y-intercept may be determined by
taking c÷b
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7. General/Standard Form
• Original Equation
2 (5 + 3y) = - (x – 4)
• Distribute -2 to (5 + 3y) on the left side and -1 to (x - 4) on
the right side.
2*5 + 2*3y = -1*x – 1*(-4)
10 + 6y = -x +4
• Subtract 10 from both sides
10 – 10 + 6y = -x + 4 – 10
6y = -x – 6
• Add x to both sides
+ x + 6y = - x + x – 6
x + 6y = -6
• Slope = (-1÷6)=-1/6; y-intercept = (-6)÷6= -1
Next
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8. General/Standard Form
• Pop Quiz!
– General/Standard form of a linear
equation is:
• A) y = mx + b
• B) ax + by = c
• C) y -y1 = m(x – x1)
(answers will be given at the conclusion)
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9. Graphing Linear Equations
• Using T- Chart:
– Pick any x-values [ I choose {-2, -1, 0, 1, 2} ] and plug them
into the linear equation to get a y-value.
• Given: y = 5x + 8
x= -2; y = 5(-2) + 8 .. y = -10 + 8 .. y = -2
x= -1; y = 5(-1) + 8 .. y = -5 + 8 .. y = 3
x= 0; y = 5(0) + 8 .. y = 0 + 8 .. y = 8
x= 1; y = 5(1) + 8 .. y = 5 + 8 .. y = 13
x= 2; y = 5(2) + 8 .. y = 10 + 8 .. y = 18
• From there, you will plot each point (-2, -2), (-1, 3), (0, 8), (1, 13), (2,
18) and connect the dots with a straight line placing arrows on
each end of the line indicating the line will continue both ways.
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10. Graphing Linear Equations
• Using slope & y-intercept
– When a linear equation is in slope intercept form, plot the y-
intercept and use the slope to guide you to other points.
• Given: y = ½x + 3
• If you start on the y-axis at the point (0, 3), use the slope to guide
you up 1 and to the right 2 to the point (2, 4). The next point
would be ( 4, 5). Then go back to
• the point (0,3) and plot a point
• down 1 and to the left 2 to (-2, -2).
The next point would be (-4, 1).
You would then connect these
dots with arrows on each end
indicating the line continues.
Next

11. Graphing Linear Equations
• Pop Quiz!
– One way to graph a linear equation is to
use the slope of the equation and y-
intercept, starting at the y-intercept and
using the slope to guide you.
• True
• False
(answers will be given at the conclusion)
Next
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12. Conclusion
• There are many types of linear equations with
multiple ways to solve and graph each equation.
• Two types of linear equations are slope-intercept
and general form.
• Two ways to graph linear equations are using a t-
chart and using the y-intercept and guiding the next
points with the slope.
• To watch a video about solving linear equations
please, visit http://patrickjmt.com/solving-linear-equations/
Pop quiz answers: 1) C 2) B 3) True
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