Answer: The slope of the line passing through the given points is− 74 , so the line perpendicular to this line has the
slope^74.
Equations of Lines
They−axis is Vertical –When using the slope-intercept form to graph a line or write an equation, it is common
for students to use thex−intercept instead of they−intercept. Remind them that they want to use the vertical axis,
y−intercept, to begin the graph. Requiring that they−intercept be written as a point, say( 0 , 3 )instead of just 3,
helps to alleviate this problem.
Where’s the Slope –Students are quickly able to identify the slope as the coefficient of thex−variable when a line
is in slope-intercept form, unfortunately they sometimes extend this to standard form. Remind the students that if
the equation of a line is in standard form, or any other form, they must first algebraically convert it to slope-intercept
form before they can easily read off the slope.
Key Exercises:
- Write the equation 3x+ 5 y=10 in slope-intercept form.
Answer:y=−^35 x+ 2
- What is the slope of the line 2x− 3 y=7?
Answer:^32
- Are the lines below parallel, perpendicular, or neither?
6 x+ 4 y= 7
6 x− 4 y= 7Answer: These lines are neither parallel nor perpendicular.
Why Use Standard Form –The slope-intercept form of the line holds so much valuable information about the
graph of a line, that students probably won’t understand why any other form would ever be used. Mention to them
that standard form is convenient when putting equations into matrices, something they will be doing in their second
year of algebra, to motivate them to learn and remember the standard form.
Perpendicular Lines
Complementary, Supplementary, or Congruent –When finding angle measures students generally need to decide
between three possible relationships: complementary, supplementary, and congruent. A good way for them to
practice with these and review their equation solving skills, is to assign variable expressions to angle measures, state
the relationship of the angles, and have the students use this information to write an equation that when solved will
lead to a numerical measurement for the angle.
Key Exercise:
- Two vertical angles have measures 2x− 30 ◦andx+ 60 ◦.
Set-up and solve an equation to findx. Then find the measures of the angles.
Answer:
2.3. Parallel and Perpendicular Lines