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Complete Table and Graph Linear Function y=-2x
Mathematics
Grade 8 (Junior High School)
Question Content
Given the linear function $y = -2x$, complete the table of values for $x = -2, -1, 0, 1, 2$ (where the value of $y$ when $x=-2$ is given as -8, which is incorrect, and you need to correct it and fill in the rest), then plot the function on the provided coordinate grid.
Correct Answer
Completed table: \n| x | -2 | -1 | 0 | 1 | 2 |\n| y | 4 | 2 | 0 | -2 | -4 |\nThe plotted line passes through points (-2,4), (-1,2), (0,0), (1,-2), (2,-4) on the coordinate grid.
Detailed Solution Steps
1
Step 1: Correct and calculate the $y$-values using the function $y=-2x$. For $x=-2$, substitute into the formula: $y=-2*(-2)=4$ (correcting the given wrong value -8).
2
Step 2: Calculate $y$ for $x=-1$: $y=-2*(-1)=2$.
3
Step 3: Calculate $y$ for $x=0$: $y=-2*0=0$.
4
Step 4: Calculate $y$ for $x=1$: $y=-2*(1)=-2$.
5
Step 5: Calculate $y$ for $x=2$: $y=-2*(2)=-4$.
6
Step 6: Plot each pair $(x,y)$ as a point on the coordinate grid, then draw a straight line connecting all the points to represent the linear function.
Knowledge Points Involved
1
Linear Function Evaluation
A linear function has the form $y=kx+b$ (where $k$ is the slope and $b$ is the y-intercept). To find the value of $y$ for a given $x$, substitute the $x$-value into the function formula and perform the arithmetic calculation. This is used to generate ordered pairs for graphing.
2
Graphing Linear Functions
To graph a linear function, first generate a table of ordered pairs $(x,y)$ by evaluating the function for different $x$-values. Then plot each ordered pair as a point on a coordinate plane, and draw a straight line through all the points. Linear functions always graph as straight lines.
3
Sign Rules for Multiplication of Integers
When multiplying two integers, if the signs are the same (positive*positive or negative*negative), the result is positive. If the signs are different (positive*negative or negative*positive), the result is negative. This rule is essential for correctly evaluating linear functions with negative coefficients, like $y=-2x$.
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