Math Problem Statement

Atrisini šo

Atrisini šo

Solution

To solve the problem based on the provided image, let’s analyze the function and its requirements:

The function is y=33xy = 3 - 3x.

1. Fill the table:

We calculate yy for the given xx-values:

  • For x=1x = 1: y=33(1)=0y = 3 - 3(1) = 0. This is already correct in the table.
  • For x=2x = 2: y=33(2)=3y = 3 - 3(2) = -3. The value in the table should be updated to -3 instead of 00.

The correct table is:

x & 1 & 2 \\ \hline y & 0 & -3 \\ \end{array}$$ --- ### 2. Determine where the graph intersects the $$OY$$-axis: To find where the graph intersects the $$OY$$-axis, set $$x = 0$$: $$y = 3 - 3(0) = 3$$ Thus, the intersection is at **(0; 3)**, which is correct. --- ### 3. Determine where the graph intersects the $$OX$$-axis: To find where the graph intersects the $$OX$$-axis, set $$y = 0$$: $$0 = 3 - 3x \implies 3x = 3 \implies x = 1$$ Thus, the intersection is at **(1; 0)**, not $$(2; 0)$$. --- ### Corrected Answers: 1. Updated table: $$\begin{array}{c|c|c} x & 1 & 2 \\ \hline y & 0 & -3 \\ \end{array}$$ 2. Intersection with $$OY$$: $$(0; 3)$$. 3. Intersection with $$OX$$: $$(1; 0)$$. Let me know if you need additional details or further clarification! --- **Further questions you can explore:** 1. How would the graph look for a larger range of $$x$$-values? 2. What is the slope of this linear function? 3. What happens if you shift the function by adding a constant (e.g., $$y = 3 - 3x + 2$$)? 4. How do you find the midpoint between the two axes' intersections? 5. What is the general form of a linear function, and how does this example fit? **Tip:** Always double-check calculations for each point when filling a table for graphing.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Coordinate Geometry

Formulas

y = mx + c (Equation of a straight line)

Theorems

Slope-intercept form of a linear equation

Suitable Grade Level

Grades 7-9