What is the slope of the line perpendicular and parallel to 7x+2y=-4?

Question

Genesis Allen · Accepted Answer

#m_("perpendicular")=2/7,m_("parallel")=-7/2# #• " parallel lines have equal slopes"# #"given a line with slope m then the slope of a line"# #"perpendicular to it is "# #•color(white)(x)m_(color(red)"perpendicular")=-1/m# #"the equation of a line in "color(blue)"slope-intercept form"# is. #•color(white)(x)y=mx+b# #"where m is the slope and b the y-intercept"# #"rearrange "7x+2y=-4" into this form"# #2y=-7x-4# #rArry=-7/2x-2" with "m=-7/2# #rArrm_(color(red)"parallel")=-7/2# #rArrm_(color(red)"perpendicular")=-1/(-7/2)=2/7#

Eva Adamson · Answer

undefined To find the slope of the line parallel to $7x + 2y = -4$, we need to rearrange the equation into slope-intercept form ($y = mx + b$) and then identify the coefficient of $x$, which represents the slope.

First, rearrange the equation:
$$2y = -7x - 4$$
$$y = -\frac{7}{2}x - 2$$

The slope of the line is $-\frac{7}{2}$.

To find the slope of the line perpendicular to $7x + 2y = -4$, we use the fact that perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of $-\frac{7}{2}$, which is $\frac{2}{7}$.