Concept explainers
(a)
To Graph :
(a)
Explanation of Solution
Given Information:
Equation of line is
Concept Used:
The slope-intercept form of a line is :
Graph:
This equation is in slope-intercept form.
Here ,
The y-intercept is the point (0,1).
Now
Steps to draw the line :
1.Start at the origin and move 1 unit up. Draw a point at (0,1) = (0,c)
2.The slope is
You are now at (4,4) = (b,c+a). Draw a point here.
3. Continue this process. Now use a ruler and connect the points and extend the line in both directions.
(b)
To Draw:
Use protrector to draw a line perpendicular to the line drawn in (a)
(b)
Explanation of Solution
Concept Used:
Construction of perpendicular lines with the help of protractor:
a. Let l be the given line and A the given point on it.
b. Place the protractor on the line l such that its base line coincides with l, and its centre falls on A.
c. Mark a point B against the 90° mark on the protractor.
d. Remove the protractor and draw a line m passing through A and B.
Then line m is perpendicular to line l at A.
Graph:
Draw a line with the help of Protractor :
Keeping (0,1) as point A in the protractor and
(c)
To Find :
Equation of line drawn in part (b)
(c)
Explanation of Solution
Concept Used:
The slope-intercept form of a line is :
Calculation:
1.Find the slope
Choose (0,1) as the point through which line passes and find the y-intercept
Write the equation using Slope Intercept form
Hence, required equation of line is
(d)
To Compare :
The slopes of lines in part (a) and (c)
(d)
Explanation of Solution
Given Information :
Equations of lines from part (a) and (c) :
Interpretation:
From part (a) and (c)
We have slopes of lines
So, we have the relation between the slopes of perpendicular lines.
The product of slopes of two perpendicular lines is -1.
Chapter 4 Solutions
Algebra 1
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