It is 120°, rotate a triangle each time adding 60 to get 120 degrees.
2n=n-5 subtract n from both sides
n=-5
check...
2(-5)=(-5)-5
-10=-10
The simplified equation in slope-intercept form of the line t that passes through (-8, -2) and is perpendicular to line s is: ![\mathbf{y = -\frac{1}{8} x - 3}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20x%20-%203%7D)
<em><u>Recall</u></em>:
- The slope-intercept form of any line can be written as:
![\mathbf{y = mx + b}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20mx%20%2B%20b%7D)
- point-slope form:
![\mathbf{y - b = m(x - a)}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20-%20b%20%3D%20m%28x%20-%20a%29%7D)
- If a line is perpendicular to another line, the slope of one will be the negative reciprocal of the other line it is perpendicular to.
<em><u>Given:</u></em>
- Line s equation: y = 8x+7
- line t passes through line s
- line t passes through a point (-8, -2)
<u><em>Thus</em></u>:
- The slope of line s,
is 8.
- The slope (m) of line t, will be the negative reciprocal of 8, which is
![-\frac{1}{8}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B8%7D)
<em>Write the </em><em>equation </em><em>of line t in </em><em>point-slope form </em><em>by substituting m = </em>
<em> and (a, b) = (-8, -2) into </em>
.
![\mathbf{y - (-2) = -\frac{1}{8} (x - (-8))}\\\\\mathbf{y + 2 = -\frac{1}{8}(x + 8)}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20-%20%28-2%29%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20%28x%20-%20%28-8%29%29%7D%5C%5C%5C%5C%5Cmathbf%7By%20%2B%202%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%28x%20%2B%208%29%7D)
<em>Rewrite the </em><em>equation </em><em>in the form of </em>![\mathbf{y = m(x - b)}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%20%3D%20m%28x%20-%20b%29%7D)
![\mathbf{y + 2 = -\frac{1}{8} (x + 8)}\\\\y + 2 = -\frac{1}{8} x - 1\\\\y + 2 - 2 = -\frac{1}{8} x - 1 - 2\\\\y = -\frac{1}{8} x - 3](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%2B%202%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20%28x%20%2B%208%29%7D%5C%5C%5C%5Cy%20%2B%202%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20x%20-%201%5C%5C%5C%5Cy%20%2B%202%20-%202%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20x%20-%201%20-%202%5C%5C%5C%5Cy%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20x%20-%203)
Therefore, the simplified equation in slope-intercept form of the line t that passes through (-8, -2) and is perpendicular to line s is: ![\mathbf{y = -\frac{1}{8} x - 3}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20-%5Cfrac%7B1%7D%7B8%7D%20x%20-%203%7D)
Learn more here:
brainly.com/question/16452396