Question

the equation of line c is y = -7x + 10. line d is perpendicular to line c and passes through (7, 4). what is the equation of line d? 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 d

The slope of line \( c \) is \( -7 \). For perpendicular lines, the product of slopes is \( -1 \). Let slope of \( d \) be \( m_d \). So, \( -7 \times m_d = -1 \), which gives \( m_d = \frac{1}{7} \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(7,4) \) and \( m=\frac{1}{7} \). Substituting, we get \( y - 4=\frac{1}{7}(x - 7) \).

Step3: Convert to slope - intercept form

Simplify \( y - 4=\frac{1}{7}x - 1 \). Add 4 to both sides: \( y=\frac{1}{7}x+3 \).

Answer:

\( y = \frac{1}{7}x + 3 \)