Given:
A line is perpendicular to the given line and having negative slope.
To find:
The slope of the line.
Solution:
We know that, product of slopes of two perpendicular lines is -1.
[tex]m_1\cdot m_2=-1[/tex]
[tex]m_1=-\dfrac{1}{m_2}[/tex]
It means, one slope is opposite and reciprocal of other.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that, blue line passes through (0,3) and (2,4). So, slope of blue line is
[tex]m_B=\dfrac{4-3}{2-0}[/tex]
[tex]m_B=\dfrac{1}{2}[/tex]
The slope of blue line is [tex]\dfrac{1}{2}[/tex]. So, slope of the line which is perpendicular to the blue line is -2, which is negative.
From the given graph it is clear that, red line passes through (0,4) and (4,3). So, slope of red line is
[tex]m_R=\dfrac{3-4}{4-0}[/tex]
[tex]m_R=\dfrac{-1}{4}[/tex]
The slope of blue line is [tex]-\dfrac{1}{4}[/tex]. So, slope of the line which is perpendicular to the blue line is 4, which is positive.
Therefore, the slope of the line which is perpendicular to the given line and having negative slope, is -2.
