First, you must find the slope, which is -5-4/-1-4, or 1.8, and then put it in point-slope form, or y-4=1.8(x-2), which simplifies to y-4=1.8x-3.6, and so put it in general/standard form, you have to subtract 1.8x from both sides and then add 4 to both sides, and lastly divide both sides of the equation by -1.8 to get x+y=1.889, or x+y=1.6/1.8. This is not copied and pasted.
The value of r so the line that passes through (-5,2) and (3,r) has a slope of -1/2 is -2
<u>Solution:</u>
Given that line is passing through point (-5, 2) and (3, r)
Slope of the line is ![\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7D)
Need to determine value of r.
Slope of a line passing through point
is given by following formula:
--- eqn 1
![\text { In our case } x_{1}=-5, y_{1}=2, x_{2}=3, y_{2}=\mathrm{r} \text { and } m=-\frac{1}{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20In%20our%20case%20%7D%20x_%7B1%7D%3D-5%2C%20y_%7B1%7D%3D2%2C%20x_%7B2%7D%3D3%2C%20y_%7B2%7D%3D%5Cmathrm%7Br%7D%20%5Ctext%20%7B%20and%20%7D%20m%3D-%5Cfrac%7B1%7D%7B2%7D)
On substituting the given value in (1) we get
![\begin{array}{l}{-\frac{1}{2}=\frac{r-2}{3-(-5)}} \\\\ {\text { Solving the above expression to get value of } r} \\\\ {=>-\frac{1}{2}=\frac{r-2}{3+5}} \\\\ {=>-8=\frac{r-2}{3+5}} \\\\ {=>-8=2(r-2)} \\\\ {=>-8=2 r-4} \\\\ {=>2 r=-8+4} \\\\ {=>2 r=-4} \\\\ {=>r=\frac{-4}{2}=-2}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B-%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7Br-2%7D%7B3-%28-5%29%7D%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Solving%20the%20above%20expression%20to%20get%20value%20of%20%7D%20r%7D%20%5C%5C%5C%5C%20%7B%3D%3E-%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7Br-2%7D%7B3%2B5%7D%7D%20%5C%5C%5C%5C%20%7B%3D%3E-8%3D%5Cfrac%7Br-2%7D%7B3%2B5%7D%7D%20%5C%5C%5C%5C%20%7B%3D%3E-8%3D2%28r-2%29%7D%20%5C%5C%5C%5C%20%7B%3D%3E-8%3D2%20r-4%7D%20%5C%5C%5C%5C%20%7B%3D%3E2%20r%3D-8%2B4%7D%20%5C%5C%5C%5C%20%7B%3D%3E2%20r%3D-4%7D%20%5C%5C%5C%5C%20%7B%3D%3Er%3D%5Cfrac%7B-4%7D%7B2%7D%3D-2%7D%5Cend%7Barray%7D)
Hence the value of "r" is -2
Everything has been explained in there
Answer:
1.= 2.5
2.= is incorrect because there should not be more than one = sign
Step-by-step explanation: