Question

У=-3х+1 побудувати графік функції

Answer 1

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Answer 2

#### Graphing the Function y = -3x + 1 To graph the function y = -3x + 1, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope of the line and b represents the y-intercept. In the given function, the slope is -3 and the y-intercept is 1. This means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 3. To plot the graph, we can choose a few x-values and calculate the corresponding y-values using the equation y = -3x + 1. Let's choose x = -3, -2, 1, and 4. When x = -3: y = -3(-3) + 1 = 9 + 1 = 10 When x = -2: y = -3(-2) + 1 = 6 + 1 = 7 When x = 1: y = -3(1) + 1 = -3 + 1 = -2 When x = 4: y = -3(4) + 1 = -12 + 1 = -11 Now, let's#### Graphing the Function y = -3x + 1 To graph the function y = -3x + 1, we can plot several points on the coordinate plane and then connect them to create a line. Let's find the values of y for different x-values. For x = -3: y = -3(-3) + 1 = 10 For x = -2: y = -3(-2) + 1 = 7 For x = 1: y = -3(1) + 1 = -2 For x = 4: y = -3(4) + 1 = -11 Now, let's plot these points on the graph: - Point A: (-3, 10) - Point B: (-2, 7) - Point C: (1, -2) - Point D: (4, -11) We can now connect these points to create the graph of the function y = -3x + 1. #### Graph of the Function y = -3x + 1  #### Finding y-values for given x-values a) To find the y-values for the given x-values (-3, -2, 1, 4), we can substitute these values into the equation y = -3x + 1: For x = -3: y = -3(-3) + 1 = 10 For x = -2: y = -3(-2) + 1 = 7 For x = 1: y = -3(1) + 1 = -2 For x = 4: y = -3(4) + 1 = -11 So, the corresponding y-values for x = -3, -2, 1, and 4 are 10, 7, -2, and -11, respectively. b) To find the x-values for the given y-values (2, 4.5, 8), we can rearrange the equation y = -3x + 1 to solve for x: For y = 2: 2 = -3x + 1 -3x = 2 - 1 -3x = 1 x = 1/(-3) x = -1/3 For y = 4.5: 4.5 = -3x + 1 -3x = 4.5 - 1 -3x = 3.5 x = 3.5/(-3) x = -7/6 For y = 8: 8 = -3x + 1 -3x = 8 - 1 -3x = 7 x = 7/(-3) x = -7/3 So, the corresponding x-values for y = 2, 4.5, and 8 are -1/3, -7/6, and -7/3, respectively. I hope this helps! Let me know if you have any further questions.