Question

If you multiply the slopes of two perpendicular lines, the product is -1.

Answer 1

$-\frac{1}{2}\cdot2=-1$

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 $y=-\frac{1}{2} x+2$.

Slope of the line g ($m_1$) = $-\frac{1}{2}$

If two lines are perpendicular, then the product of the slopes is –1.

⇒ $m_1 \cdot m_2=-1$

To find the slope of the line h:

$\Rightarrow-\frac{1}{2} \cdot m_2=-1$

$\Rightarrow m_2=-1 \times(-2)$

$\Rightarrow m_2=2$

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:

$\left(y-y_{1}\right)=m\left(x-x_{1}\right)$

$\left(y-4)=2\left(x-0\right)$

$y-4=2x$

$y=2x+4$

The equation for line h is y = 2x + 4.