How do you find the slope and intercept for #x+10y=7#?

Question

Nathan Axel · Accepted Answer

Convert to slope-intercept form and pull the correct values from this form of the equation. See the full explanation below.

To find the slope and y-intercept we will transform this equation to the slope-intercept form by solving for #y#: The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)# Where #color(red)(m)# is the slope and #color(blue)(b# is the y-intercept value. #x + 10y = 7# #x - color(green)(x) + 10y = - color(green)(x) + 7# #0 + 10y = - color(green)(x) + 7# #10y = - color(green)(x) + 7# #(10y)/color(green)(10) = (-color(green)(x) + 7)/color(green)(10)# #(color(green)(cancel(color(black)(10)))y)/cancel(color(green)(10)) = -1/10x + 7/10# #y = color(red)(-1/10)x + color(blue)(7/10)# The slope is #m = color(red)(-1/10)# The y-intercept is #b = color(blue)(7/10)#

Avery Alexander · Answer

undefined To find the slope and intercept for the equation $x + 10y = 7$, rearrange it into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept:
$$10y = -x + 7$$
Divide both sides by 10 to isolate $y$:
$$y = -\frac{1}{10}x + \frac{7}{10}$$
So, the slope $m$ is $-\frac{1}{10}$ and the y-intercept $b$ is $\frac{7}{10}$.