Question

Y=2x-4 встановити її властивості і побудували графік

Answer 1

Ответ в файле

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Answer 2

The given equation is Y = 2x - 4, which represents a straight line in the Cartesian coordinate system. This equation is in slope-intercept form (Y = mx + b), where "m" is the slope of the line, and "b" is the y-intercept (the value of Y when x = 0).

Properties of the equation Y = 2x - 4:

1. Slope: The slope of the line is 2. This means that for every one unit increase in the x-coordinate, the y-coordinate will increase by 2 units. The slope indicates the direction and steepness of the line.

2. Y-intercept: The y-intercept occurs when x = 0. Substituting x = 0 into the equation, we get: Y = 2(0) - 4 Y = -4 So, the y-intercept is (0, -4), meaning the line crosses the y-axis at this point.

3. x-intercept: The x-intercept occurs when Y = 0. Setting Y = 0 and solving for x: 0 = 2x - 4 2x = 4 x = 2 So, the x-intercept is (2, 0), meaning the line crosses the x-axis at this point.

4. Line behavior: Since the equation is in the form Y = mx + b, the line is a straight line, and it will continue indefinitely in both directions.

Now, let's plot the graph:

To plot the graph, we can choose some x-values, calculate the corresponding y-values using the equation, and then plot the points. We can also use the intercepts we found earlier to plot the line more accurately.

Let's choose some x-values and calculate the corresponding y-values:

x = -2: Y = 2(-2) - 4 = -4 - 4 = -8 x = -1: Y = 2(-1) - 4 = -2 - 4 = -6 x = 0: Y = 2(0) - 4 = 0 - 4 = -4 x = 1: Y = 2(1) - 4 = 2 - 4 = -2 x = 2: Y = 2(2) - 4 = 4 - 4 = 0

Now, we can plot the points (-2, -8), (-1, -6), (0, -4), (1, -2), and (2, 0) on the graph and draw a straight line passing through these points.

The graph of the equation Y = 2x - 4 is a straight line with a slope of 2 and a y-intercept of (0, -4). It passes through the points (-2, -8), (-1, -6), (0, -4), (1, -2), and (2, 0).

Please note that the graph extends infinitely in both directions, but we typically only plot a portion of it to fit within the graphing area.

I apologize for the limitations of text in representing the actual graph visually, but I hope the information provided helps you understand the properties of the given equation and its graphical representation.