the equation of line s is ( y = -\frac{1}{9}x - 4 ). line t includes the point ( (1,7) ) and is…

the equation of line s is ( y = -\frac{1}{9}x - 4 ). line t includes the point ( (1,7) ) and is perpendicular to line s. what is the equation of line t? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

the equation of line s is ( y = -\frac{1}{9}x - 4 ). line t includes the point ( (1,7) ) and is perpendicular to line s. what is the equation of line t? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer

Explanation:

Step1: Find the slope of line (t)

The slope of line (s) is (m_s =-\frac{1}{9}). If two lines are perpendicular, the product of their slopes is (- 1), i.e., (m_s\times m_t=-1). Let the slope of line (t) be (m_t). Then (-\frac{1}{9}\times m_t=-1), so (m_t = 9).

Step2: Use the point - slope form to find the equation of line (t)

The point - slope form of a line is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(1,7)) and (m = 9). Substitute these values into the formula: (y - 7=9(x - 1)).

Step3: Convert to slope - intercept form

Expand the right - hand side: (y-7 = 9x-9). Add (7) to both sides of the equation: (y=9x-9 + 7).

Answer:

(y = 9x-2)