Transcript Slide 1

Modeling with Linear Equations
MATH 102
Contemporary Math
S. Rook
Overview
• Section 7.2 in the textbook:
– Building equations with a point and a slope
– Building equations using two points
Building Equations with a Point
and a Slope
Building Equations with a Point and
a Slope
• Recall the slope-intercept form of a line
y = mx + b
• What is the significance of m & b?
• Recall that points are comprised of two parts:
– The x-part and y-part
• Given the slope m and a point, we can solve for b
• Finally, we obtain an equation by filling in the values
for m & b and keeping x & y as variables
– e.g. Find the equation of a line with a slope of 1 and
passes through (3, 2)
Building Equations with a Point and
a Slope (Example)
Ex 1: Find a linear equation with the given point
and slope:
a) Slope 4; Point (-2, 6)
b) Slope -8; Point (-4, -9)
Building Equations Using Two
Points
Building Equations Using Two
Points
• If we are given only two points, what element
are we missing?
• How do we calculate the slope between two
points?
• We now have a choice of which point to use in
the slope-intercept formula
– It does not matter which point is used – the same
equation will result
7
Building Equations Using Two
Points (Example)
Ex 2: Find a linear equation that passes through
the given points:
a) (17, 12) and (9, 10)
b) (11, -4) and (-8, 2)
Building Equations Using Two
Points (Example)
Ex 3: According to the Consumer Electronics
Association, the number of direct satellite dish
receivers rose from 4.3 million in 2000 to 16.8
million in 2004.
a) Construct a linear equation relating the year to
the number of satellite dishes
b) In which year will there be 40 million receivers?
Summary
• After studying these slides, you should know
how to do the following:
– Write a linear equation given the slope and a
point
– Write a linear equation given two points
• Additional Practice:
– See problems for Section 7.2
• Next Lesson:
– Systems of Linear Equations (Section 8.1)