How do you find the slope and y intercept of #3x-7y=20#?

Question

Avery Alexander · Accepted Answer

#"slope "=3/7," y-intercept "=-20/7# #"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 "3x-7y=20" into this form"# #"subtract "3x" from both sides"# #-7y=-3x+20# #"divide all terms by "-7# #y=3/7x-20/7larrcolor(blue)"in slope-intercept form"# #"with slope "=3/7" and y-intercept "=-20/7#

Savannah Anderson · Answer

Slope=#3/7#

#y#-intercept: #-20/7# To find the slope and #y#-intercept, we need to change this equation into slope-intercept form #y=mx+b# where #m# is the slope and #b# is the #y#-intercept. We can start by subtracting #3x# from both sides to get #-7y=-3x+20# Lastly, we divide all terms by #-7# to get #y=3/7x-20/7# Our #m# in this case is #3/7#. This is the slope. Our #b# in this case is #-20/7#. This is our #y#-intercept. Hope this helps!

Jace Anderson · Answer

undefined To find the slope and y-intercept of the equation $3x - 7y = 20$, we first rearrange the equation into slope-intercept form, $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

To isolate $y$, we subtract $3x$ from both sides of the equation:

$$3x - 3x - 7y = -3x + 20$$
$$-7y = -3x + 20$$

Then, we divide both sides by $-7$ to solve for $y$:

$$y = \frac{-3x + 20}{-7}$$

Now, we can identify the slope $m$ by comparing the equation to $y = mx + b$. The coefficient of $x$ is the slope $m$.

$$m = \frac{-3}{-7} = \frac{3}{7}$$

To find the y-intercept $b$, we observe that when $x = 0$, $y$ is equal to the y-intercept. Substituting $x = 0$ into the equation:

$$y = \frac{-3(0) + 20}{-7} = \frac{20}{-7} = -\frac{20}{7}$$

Therefore, the slope $m$ is $3/7$ and the y-intercept $b$ is $-20/7$.