Question

How do i write the slope-intercept form of: through: (-4,-2), perpendicular to y=7x+4

Answer 1

let's take a peek at 7x + 4 for a second,
`\bf y = \stackrel{slope}{7}x\stackrel{y-intercept}{+4}`

well well, it has a slope of 7.

now, a line perpendicular to that one, will have a negative reciprocal slope,


`\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad 7\implies \cfrac{7}{1}\\\\ negative\implies -\cfrac{7}{{{ 1}}}\qquad reciprocal\implies - \cfrac{{{ 1}}}{7}`

so, we're really looking for the equation of a line whose slope is -1/7 and runs through -4, -2