Question

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.

(9, 12); y=13x−4

Answer 1

`\sf y = (-1)/(13)x+ (165)/(13)`

Explanation:

Equation of line in slope-intercept form: y = mx + b

Here m is the slope and b is the y-intercept.

y = 13x - 4

m₁ = 13

Product of slope of the Perpendicular line m * m₁ = -1

`\sf m = (-1)/(m_1)\\\\m = (-1)/(13)`

Equation of the line:

`\sf y = (-1)/(13)x+b`

The point (9,12) passes through the line. Substitute the coordinates in the above equation and find the value of 'b'.

`\sf 12 = (-1)/(13)*9+b\\\\`

`\sf 12 + (9)/(13)=b\\\\ (156)/(13)+ (9)/(13)=b\\\\\boxed{b= (165)/(13)}`

Equation of line:

`\sf y = (-1)/(13)x+ (165)/(13)`