Question

Which equation in point-slope form contains the point (–2, –6) and has slope –4?

Answer 1

now, on another posting, you were asking what's the slope of a line perpendicular to another through (-3,2)(0,-2)?

ok, lemme post that here then





`\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\ \textit{so a perpendicular slope to a line with }-\cfrac{4}{3}\textit{ will be} \\\\\\ negative\implies \cfrac{4}{3}\qquad reciprocal\implies \boxed{\cfrac{3}{4}}`

Answer 2

`y+6 = -4(x+2)`

Explanation:

Point slope form:

The equation of straight line passes through the given point
`(x_1, y_1)` is given by:-

`y-y_1=m(x-x_1)` .....[1]

where, m is the slope of the line.

As per the statement:

Given the point (-2, -6) and has slope -4.

Substitute the given values in [1] we have;

`y-(-6)=-4(x-(-2))`

`y+6 = -4(x+2)`

Therefore, the equation in point-slope form contains the point (–2, –6) and has slope –4 is,
`y+6 = -4(x+2)`