Question

ДАЮ 25 БАЛЛОВ, РЕШИТЕ БЫСТРЕЕ ПЛЗ!!! Задайте формулой линейную функцию, графиком которой служит прямая, проходящая через точку А(2;3) и параллельная графику функции y=1.5x-3. Постройте график.

Answer 1

Так как по условию прямая должна быть параллельна прямой у=1,5х-3 и угловые коэффициенты параллельных прямых равны, то общая формула для всех таких прямых
у=1,5х+b
Чтобы найти b подставим координаты точки А
х=2    у=3
3=1,5·2+b    ⇒  b=0
Ответ. формулой  у=1,5х задается линейная функция, графиком которой служит прямая, проходящая через точку А(2;3) и параллельная графику функции y=1.5x-3.
Для построения прямой достаточно двух точек:
(0;0) и (2;3)

Answer 2

To find the equation of a line parallel to the graph of the function y = 1.5x - 3 and passing through the point A(2, 3), we can use the fact that parallel lines have the same slope.

The given function y = 1.5x - 3 has a slope of 1.5. Therefore, the parallel line we are looking for will also have a slope of 1.5.

Using the point-slope form of a linear equation, we can write the equation of the line as:

y - y1 = m(x - x1)

where (x1, y1) is the given point A(2, 3) and m is the slope of the line.

Substituting the values into the equation, we have:

y - 3 = 1.5(x - 2)

Now, let's simplify this equation to find the equation of the line.

Simplifying the equation:

Expanding the right side of the equation:

y - 3 = 1.5x - 3

Combining like terms:

y = 1.5x

So, the equation of the line parallel to the graph of y = 1.5x - 3 and passing through the point A(2, 3) is y = 1.5x.

Now, let's plot the graph of this line.

Graph:

To plot the graph, we can choose some x-values and calculate the corresponding y-values using the equation y = 1.5x.

Let's choose x = -2, -1, 0, 1, 2, and 3.

For x = -2: y = 1.5 * (-2) = -3

For x = -1: y = 1.5 * (-1) = -1.5

For x = 0: y = 1.5 * 0 = 0

For x = 1: y = 1.5 * 1 = 1.5

For x = 2: y = 1.5 * 2 = 3

For x = 3: y = 1.5 * 3 = 4.5

Now, let's plot these points on a graph:

   ^
   |        .
   |      .
   |    .
   |  .
   |_______________________
   -2  -1  0  1  2  3  4

The graph of the line y = 1.5x is a straight line passing through the origin (0, 0) and having a slope of 1.5. Since the line is parallel to the graph of y = 1.5x - 3, it will have the same slope but a different y-intercept.

Please note that the graph is not drawn to