Math Problem Statement

Give me the answer for this question

Give me the answer for this question

Solution

The problem is asking you to fill in the values for the table and plot the graph of the linear equation y=2x+5y = 2x + 5.

Let's calculate the values of yy for each value of xx given in the table:

  1. When x=−2x = -2: y=2(−2)+5=−4+5=1y = 2(-2) + 5 = -4 + 5 = 1

  2. When x=−1x = -1: y=2(−1)+5=−2+5=3y = 2(-1) + 5 = -2 + 5 = 3

  3. When x=0x = 0: y=2(0)+5=0+5=5y = 2(0) + 5 = 0 + 5 = 5

  4. When x=1x = 1: y=2(1)+5=2+5=7y = 2(1) + 5 = 2 + 5 = 7

  5. When x=2x = 2: y=2(2)+5=4+5=9y = 2(2) + 5 = 4 + 5 = 9

Now, let's fill in the table with these values:

x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 1 & 3 & 5 & 7 & 9 \\ \end{array}$$ To draw the graph, plot these points on the coordinate grid: - $$(-2, 1)$$ - $$(-1, 3)$$ - $$(0, 5)$$ - $$(1, 7)$$ - $$(2, 9)$$ These points will form a straight line since the equation $$y = 2x + 5$$ represents a linear function. Would you like any further details or have any questions? Here are some related questions: 1. How do you determine the slope of a line from its equation? 2. What is the y-intercept of the equation $$y = 2x + 5$$? 3. How would you plot a graph for a quadratic function? 4. How does the value of the coefficient $$2$$ affect the graph's steepness? 5. What are some other methods to graph a linear equation? **Tip:** Remember, the coefficient of $$x$$ in a linear equation $$y = mx + b$$ is the slope, and it shows how steep the line is.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

y = 2x + 5

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-9

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