Math Problem Statement

is my drow right

Graph the equation x + 5y = 20 and identify the y-intercept. Is my drawing correct?

Solution

Let's analyze the task based on the images:

  1. First image: You plotted the graph, and the yellow vertical line at x=0x = 0 seems to represent the y-axis. The blue dot at (0,4)(0, 4) corresponds to the y-intercept.

  2. Second image: The problem involves graphing the equation x+5y=20x + 5y = 20 and identifying the y-intercept.

    To determine the y-intercept, we can set x=0x = 0 in the equation x+5y=20x + 5y = 20: 0+5y=20    y=205=40 + 5y = 20 \implies y = \frac{20}{5} = 4 So, the y-intercept is (0,4)(0, 4), which matches the point marked in your graph.

Therefore, your drawing is correct: the y-intercept is indeed (0,4)(0, 4).

Do you have any questions or would you like further clarification?

Here are 5 related questions to further expand your understanding:

  1. What would be the slope of the line represented by x+5y=20x + 5y = 20?
  2. How do you find the x-intercept for the same equation?
  3. Can you rewrite the equation x+5y=20x + 5y = 20 in slope-intercept form?
  4. What would happen to the graph if the equation were x+5y=15x + 5y = 15?
  5. How does changing the coefficient of yy in the equation affect the slope of the line?

Tip: Always double-check by substituting points from the graph into the equation to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Linear Equations

Formulas

x + 5y = 20
Slope-intercept form: y = mx + b

Theorems

Slope-intercept Theorem

Suitable Grade Level

Grades 8-10