Question

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

Explanation:

Step1: Find slope of perpendicular line

The slope of $y=2x$ is $m_1=2$. For perpendicular lines, $m_2 = -\frac{1}{m_1}$, so $m_2 = -\frac{1}{2}$.

Step2: Identify point on line L

From the graph, line L passes through $(-1,-2)$.

Step3: Write point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-\frac{1}{2}$, $x_1=-1$, $y_1=-2$.
$y - (-2) = -\frac{1}{2}(x - (-1))$ simplifies to $y + 2 = -\frac{1}{2}(x + 1)$

Step4: Convert to slope-intercept form

Expand and solve for $y$:
$y + 2 = -\frac{1}{2}x - \frac{1}{2}$
$y = -\frac{1}{2}x - \frac{1}{2} - 2$
$y = -\frac{1}{2}x - \frac{5}{2}$

Answer:

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