write an equation for line l in point - slope form and slope - intercept form. l is perpendicular to y = 2x.

Explanation:

Step1: Find the slope of line L

If two lines are perpendicular, the product of their slopes is - 1. The slope of the line $y = 2x$ is $m_1=2$. Let the slope of line L be $m_2$. Then $2m_2=-1$, so $m_2 =-\frac{1}{2}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. The line L passes through the point $(1,2)$ and has a slope $m =-\frac{1}{2}$. So the point - slope form is $y - 2=-\frac{1}{2}(x - 1)$.

Step3: Write the slope - intercept form

Start with the point - slope form $y - 2=-\frac{1}{2}(x - 1)$. Expand the right side: $y-2=-\frac{1}{2}x+\frac{1}{2}$. Then add 2 to both sides to get the slope - intercept form $y=-\frac{1}{2}x+\frac{1}{2}+2=-\frac{1}{2}x+\frac{5}{2}$.

Answer:

Point - slope form: $y - 2=-\frac{1}{2}(x - 1)$ Slope - intercept form: $y=-\frac{1}{2}x+\frac{5}{2}$