Question

line k has an equation of $y = -\frac{2}{5}x + 10$. line $l$, which is perpendicular to line k, includes the point (1, 7). what is the equation of line $l$?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line \( l \)

The slope of line \( k \) is \( -\frac{2}{5} \). For perpendicular lines, the slope of \( l \) (\( m_l \)) is the negative reciprocal: \( m_l=\frac{5}{2} \).

Step2: Use point - slope form

Point - slope form is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(1,7) \) and \( m = \frac{5}{2} \).
Substitute values: \( y - 7=\frac{5}{2}(x - 1) \).

Step3: Convert to slope - intercept form

Expand: \( y - 7=\frac{5}{2}x-\frac{5}{2} \).
Add 7 to both sides: \( y=\frac{5}{2}x-\frac{5}{2}+7 \).
Simplify \( 7=\frac{14}{2} \), so \( y=\frac{5}{2}x+\frac{14 - 5}{2}=\frac{5}{2}x+\frac{9}{2} \).

Answer:

\( y=\frac{5}{2}x+\frac{9}{2} \)