[tex]$-\frac{1}{2}\cdot2=-1[/tex]
Slope of the line h is 2.
The equation for line h is y = 2x + 4.
Solution:
General equation of a line is y = mx + c,
where m is the slope of the line and c is the y-intercept.
In the given image, line g and line h are intersecting lines and perpendicular to each other.
Equation of line g is [tex]y=-\frac{1}{2} x+2[/tex].
Slope of the line g ([tex]m_1[/tex]) = [tex]-\frac{1}{2}[/tex]
If two lines are perpendicular, then the product of the slopes is –1.
⇒ [tex]m_1 \cdot m_2=-1[/tex]
To find the slope of the line h:
[tex]$\Rightarrow-\frac{1}{2} \cdot m_2=-1[/tex]
[tex]$\Rightarrow m_2=-1 \times(-2)[/tex]
[tex]$\Rightarrow m_2=2[/tex]
Slope of the line h is 2.
To find the equation of a line h:
Line h passing through the point (0, 4) and slope 2.
Point-slope formula:
[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]
[tex]\left(y-4)=2\left(x-0\right)[/tex]
[tex]y-4=2x[/tex]
[tex]y=2x+4[/tex]
The equation for line h is y = 2x + 4.
