Question

Use the given conditions to write an equation for the line in point slope form and general form.

Passing through (6,-4) and perpendicular to the line whose equation is x-7y-9=0

The equation of the line in point slope form is _________

Answer 1

Explanation:

point-slope form is

y - y1 = a(x - x1)

with a being the slope, and (x1,y1) being a point on the line.

the general form is

y = ax + b

a is again the slope. and b is the y-intercept (the y value when x = 0).

the slope is the ratio "y coordinate change / x coordinate change".

so, we need to find the slope of the original line :

x - 7y - 9 = 0

x - 9 = 7y

y = 1/7 x - 9/7

so, the original slope is 1/7.

the perpendicular slope turns the original slope upside-down and flips the sign.

so, it is

-7/1 = -7

the point slope form is

y - -4 = -7(x - 6)

y + 4 = -7(x - 6)

for the standard form we only need to do the multiplications and transform the equation into the above form :

y + 4 = -7(x - 6)

y + 4 = -7x + 42

y = -7x + 38