The equation given is:

$4x + 5y = 20$

This is a linear equation in two variables ($x$ and $y$). There are multiple ways to interpret and solve it:

1. Express $y$ in terms of $x$ (Slope-Intercept Form)

Rearrange the equation:

$5y = 20 - 4x$

$y = \frac{-4x + 20}{5}$

$y = -\frac{4}{5}x + 4$

This equation represents a straight line with:

• Slope: $-\frac{4}{5}$
• Y-intercept: $4$ (the point (0,4) on the y-axis)

2. Find Intercepts

• X-Intercept (set $y = 0$):

  $4x + 5(0) = 20$

  $4x = 20$

  $x = 5$

  So the x-intercept is $(5,0)$.

• Y-Intercept (set $x = 0$):

  $4(0) + 5y = 20$

  $5y = 20$

  $y = 4$

  So the y-intercept is $(0,4)$.

3. Plotting the Line

The equation represents a straight line passing through the points:

• $(5,0)$ (x-intercept)
• $(0,4)$ (y-intercept)

Would you like a graph of this equation? Let me know if you have any questions!

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Related Questions:

1. How do you convert a linear equation to standard form?
2. How do you find the equation of a line given two points?
3. What is the meaning of the slope in a linear equation?
4. How can you determine if two lines are parallel or perpendicular?
5. How do you solve a system of equations with two variables?

Tip: The slope $m$ in the equation $y = mx + b$ determines the steepness and direction of the line.