To do so, get every part into slope-intercept form (y = mx + b).
If the slopes are different, there is one solution.
If the slopes the same but the y intercepts different, there is no solution.
If the slopes and y intercepts are the same, there are infinitely many solutions.
2x + y = 4
2y = 6 - 2x
Solve for y on both
y = 4 - 2x
y = 3 - x
They are both different, so there is one solution
Answer:
<h2>y = 3x - 5</h2>
Step-by-step explanation:
![\text{The slope-intercept form of an equation of a line:}\\y=mx+b\\m-slope\\b-y\ intercept](https://tex.z-dn.net/?f=%5Ctext%7BThe%20slope-intercept%20form%20of%20an%20equation%20of%20a%20line%3A%7D%5C%5Cy%3Dmx%2Bb%5C%5Cm-slope%5C%5Cb-y%5C%20intercept)
![\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20formula%20of%20a%20slope%3A%7D%5C%5C%5C%5Cm%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\=========================](https://tex.z-dn.net/?f=%5Ctext%7BLet%7D%5C%20k%3Ay%3Dm_1x%2Bb_1%2C%5C%20l%3Ay%3Dm_2x%2Bb_2%2C%5C%20%5Ctext%7Bthen%7D%5C%5C%5C%5Cl%5C%20%5Cperp%5C%20k%5Ciff%20m_1m_2%3D-1%5Cto%20m_2%3D-%5Cdfrac%7B1%7D%7Bm_1%7D%5C%5C%5C%5Cl%5C%20%5Cparallel%5C%20k%5Ciff%20m_1%3Dm_2%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![\text{From the graph we have two points (-3, 2) and (0, 1).}\\\text{Calculate the slope of the given line:}\\\\m=\dfrac{1-2}{0-(-3)}=\dfrac{-1}{3}=-\dfrac{1}{3}.\\\\\text{Therefore the slope of the perpendicular line is:}\\\\m=-\dfrac{1}{-\frac{1}{3}}=3\\\\\text{Put it and the coordinates of the point (3, 4) to the equation of a line:}\\\\4=3(3)+b\\4=9+b\qquad\text{subtract 9 from both sides}\\-5=b\to b=-5\\\\\text{Finally:}\\\\y=3x-5](https://tex.z-dn.net/?f=%5Ctext%7BFrom%20the%20graph%20we%20have%20two%20points%20%28-3%2C%202%29%20and%20%280%2C%201%29.%7D%5C%5C%5Ctext%7BCalculate%20the%20slope%20of%20the%20given%20line%3A%7D%5C%5C%5C%5Cm%3D%5Cdfrac%7B1-2%7D%7B0-%28-3%29%7D%3D%5Cdfrac%7B-1%7D%7B3%7D%3D-%5Cdfrac%7B1%7D%7B3%7D.%5C%5C%5C%5C%5Ctext%7BTherefore%20the%20slope%20of%20the%20perpendicular%20line%20is%3A%7D%5C%5C%5C%5Cm%3D-%5Cdfrac%7B1%7D%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D3%5C%5C%5C%5C%5Ctext%7BPut%20it%20and%20the%20coordinates%20of%20the%20point%20%283%2C%204%29%20to%20the%20equation%20of%20a%20line%3A%7D%5C%5C%5C%5C4%3D3%283%29%2Bb%5C%5C4%3D9%2Bb%5Cqquad%5Ctext%7Bsubtract%209%20from%20both%20sides%7D%5C%5C-5%3Db%5Cto%20b%3D-5%5C%5C%5C%5C%5Ctext%7BFinally%3A%7D%5C%5C%5C%5Cy%3D3x-5)
Answer:
the answer is
Step-by-step explanation:
....
Answer:
50.90 cm
Step-by-step explanation:
The computation of the circumference of this circle is shown below:
As we know that
The circumference of this circle is
= 2πr
where
π is 3.142
r = diameter ÷ 2
= 16.8 ÷ 2
= 8.1 cm
So, the circumference of the circle is
= 2 × 3.142 × 8.1 cm
= 50.90 cm