How do you find the slope of 7x+2y=6?

Question

Julia Adams · Accepted Answer

#"slope "=-7/2#

The equation of a line in #color(blue)"slope-intercept form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))# where m represents the slope and b, the y-intercept.

#"Rearrange "7x+2y=6" into this form"#

From both sides of the equation, subtract 7x.

#cancel(7x)cancel(-7x)+2y=6-7x=-7x+6#

#rArr2y=-7x+6#

divide every term by two on each side.

#(cancel(2) y)/cancel(2)=(-7)/2x+6/2#

#rArry=-7/2x+3larr" in form y =mx +b"#

#rArr"slope "=m=-7/2#

Kennedy Adams · Answer

undefined To find the slope of the line represented by the equation $7x + 2y = 6$, rearrange the equation into slope-intercept form $y = mx + b$, where $m$ represents the slope.

First, isolate $y$ on one side:
$$ 2y = -7x + 6 $$

Then, divide both sides by $2$:
$$ y = -\frac{7}{2}x + 3 $$

The coefficient of $x$, which is $-\frac{7}{2}$, represents the slope of the line. So, the slope of the line is $-\frac{7}{2}$.