Укажите точки, принадлежащие графику функции \(\displaystyle y=-0{,}5x{\small.}\)
точка \(\displaystyle (x;y)\) | уравнение \(\displaystyle y=-0{,}5x\) | результат |
| \(\displaystyle A(0;1)\) | \(\displaystyle 1 \overset{\color{red}{\large?}}=-0{,}5 \cdot 0{\small;}\) \(\displaystyle 1=0\) |
неверно |
| \(\displaystyle B(-1;0{,}5)\) | \(\displaystyle 0{,}5 \overset{\color{red}{\large?}}=-0{,}5 \cdot (-1){\small;}\) \(\displaystyle 0{,}5=0{,}5\) |
верно |
| \(\displaystyle C(2;-1)\) | \(\displaystyle -1 \overset{\color{red}{\large?}}=-0{,}5 \cdot 2{\small;}\) \(\displaystyle -1=-1\) |
верно |
| \(\displaystyle D(4;-2)\) | \(\displaystyle -2 \overset{\color{red}{\large?}}=-0{,}5 \cdot 4{\small;}\) \(\displaystyle -2=-2\) |
верно |
Верное равенство получилось при подстановке координат точек
\(\displaystyle B(-1;0{,}5){\small,}\) \(\displaystyle C(2;-1)\) и \(\displaystyle D(4;-2){\small.}\)
Значит, эти точки принадлежат графику прямой пропорциональности \(\displaystyle y=-0{,}5x{\small.}\)
Ответ: \(\displaystyle B(-1;0{,}5){\small,}\) \(\displaystyle C(2;-1)\) и \(\displaystyle D(4;-2){\small.}\)