How do you find the slope of the line with the given information A) #2x+y=7# B) the line is perpendicular to #y=10x + 7#?

Question

How do you find the slope of the line with the given information A) #2x+y=7#   B) the line is perpendicular to #y=10x + 7#?

Genesis Allen · Accepted Answer

We first rewrite the first equation in slope-intercept form. (A) This is quite easy: subtract #2x# from both sides:
#y=-2x+7# so the slope is #-2# (B) If two lines are perpendicular, multiplying their slopes will allways give a result of #-1#. Let's call the slope we want to find #m#
The equation is allready in slope-intercept form with a slope of #10#. So: #m*10=-1->m=-1/10#

Nathan Axel · Answer

undefined To find the slope of a line given by the equation $2x + y = 7$, first solve for $y$ to put it in slope-intercept form, $y = mx + b$, where $m$ is the slope.

$$2x + y = 7 \Rightarrow y = -2x + 7$$

Thus, the slope of this line is $-2$.

For part B, if the line is perpendicular to $y = 10x + 7$, then its slope will be the negative reciprocal of the slope of $y = 10x + 7$. The slope of $y = 10x + 7$ is $10$, so the slope of the line that is perpendicular to it will be $-\frac{1}{10}$.