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dezoksy [38]
3 years ago
10

Write an equation in slope-intercept form for the line that is parallel to y=−4x−3 and that passes through the point (−2,4).

Mathematics
1 answer:
kirill115 [55]3 years ago
8 0

Answer:

The Correct option is Last one y=-4x-4

Therefore, equation of the line in slope-intercept that passes through (-2,4) and is parallel to the line y=-4x-3 is y=-4x-4

Step-by-step explanation:

Given:

y=-4x-3

To Find:

Equation of line passing through ( -2, 4) and is parallel to the line y=-4x-3

Solution:

y=-4x-3 ..........Given

Comparing with Slope-Intercept form,  

y=mx+c

Where m =slope  

We get

Slope = m = -4

We know that parallel lines have Equal slopes.

Therefore the slope of the required line passing through (-2 , 4) will also have the slope = m = -4.

Now the equation of line in slope point form given by

(y-y_{1})=m(x-x_{1})

Substituting the points and so we will get the required equation of the line,

(y-4))=-4(x-(-2))=-4x-8\\\\y=-4x-8+4=-4x-4\\\\y=-4x-4......Equation\ of\ line

Therefore, equation of the line in slope-intercept that passes through (-2,4) and is parallel to the line y=-4x-3 is y=-4x-4

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katovenus [111]

Answer:  see below

<u>Step-by-step explanation:</u>

17) 5n - 3 > -2n + 4     and    9 - 4n ≥ -2n + 1

   <u> +2n   </u>    <u> +2n      </u>              <u>    +2n </u>   <u>+2n      </u>

   7n - 3   >     4                    9 - 2n  ≥       1

        +3         +3                  -9                 -9

    7n       >      7                       -2n   ≥     -8

  <u> ÷7     </u>    <u>     ÷7  </u>                   <u> ÷ -2 </u>  ↓  <u> ÷ -2 </u>

          n  >     1         and            n   ≤   4                  

Graph:   o----------------- ·

              1                     4

18) 9k - 2 ≤ 9 + 10k < 9 - 4k

     9k - 2 ≤ 9 + 10k      and     9 + 10k < 9 - 4k

  <u> -10k     </u>    <u>     -10k </u>               <u>       +4k </u>   <u>    +4k  </u>

     -k - 2 ≤ 9                             9 + 14k < 9

   <u>      +2</u>   <u>+2         </u>                 <u> -9          </u>  <u>-9         </u>

     -k      ≤  11                                  14k  <  0

 <u> ÷ -1    </u>   ↓<u> ÷ -1  </u>                      <u>       ÷14 </u>    <u>÷14      </u>

          k  ≥ -11                and               k < 0

Graph:    · -----------------o

              -11                  0    

19) 4 - n ≤ 10 + 5n ≤ 6n + 1

     4 - n ≤ 10 + 5n       and     10 + 5n ≤  6n + 1

   <u>    -5n </u>   <u>      -5n  </u>                 <u>      -6n </u>   <u>-6n     </u>

   4 - 6n ≤ 10                           10  -  n  ≤       1    

  <u>-4        </u>  <u> -4            </u>              <u> -10        </u>    <u>  -10  </u>

        -6n ≤ 6                                    -n ≤   -9

   <u>  ÷ -6   </u>↓ <u>÷ -6     </u>                    <u>    ÷ -1 </u>↓<u> ÷ -1    </u>

           n ≥ -1              and                 n ≥ 9

Graph:    · -----------------→

              -9                  

20) 4p - 5 ≤ 2p + 9 ≤ 4p + 7

     4p - 5 ≤ 2p + 9     and     2p + 9 ≤ 4p + 7

  <u> -2p       </u>   <u>-2p    </u>                 <u> -4p    </u>   <u>-4p      </u>

    2p - 5 ≤         9                -2p + 9  ≤        7    

    <u>      +5   </u>  <u>    +5    </u>             <u>        -9  </u>    <u>     -9  </u>

       2p  ≤       14                   -2p       ≤      -2

   <u>  ÷ 2   </u>   <u>    ÷ 2     </u>               <u>÷ -2    </u> ↓<u>    ÷ -2    </u>

         p ≤       7          and         p    ≥      1

Graph:    · ----------------- ·

              1                    7

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Step-by-step explanation:

7 + x = 18

<em>Subtract 7 from both sides</em>

x=11

It's quite simple because if you do something to one side of the equation, you need to do it to the other because otherwise the equation won't be equal. This is how you need to simplify most problems, by taking something from one side and taking from the other as well.

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