Як знайти рівняння прямої через точку, яка паралельна заданій?

For this explanation, I am going to assume that the reader knows what slope is. By the definition of parallel lines, two lines will be parallel iff their slopes are equal. Let's say we are given the slope of a line, and let's call this slope $m$. By the definition of slope, we have $m=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}$ Let's say we are given that this line passes through the point $(a,b)$. Any point on this line can be expressed as $(x,y)$. From our equation for slope, we have that $y_{1}-y_{2}=m(x_{1}-x_{2})$ (We can assume that $x_{1}-x_{2} \neq 0$ as otherwise we would be looking at the slope between a point and itself.) If we let $x_{1} = x$ and $y_{1} = y$, we get the equation $y-y_{2} = m(x-x_{2})$ If only we knew a point that was on this line, we could get an equation for $y$ in terms of $x$. However, we were given that $(a,b)$ is on this line! Plugging this in we get $y-b=m(x-a)$ This equation is known as point slope form, and it can be useful for simplifying calculations in certain questions. Remember not to memorize this formula, instead know how to derive it so you can find it when you need it. Here are a few questions to help you learn to use this equation for a line:

Remember, don't memorize formulas, instead understand them.