How do you rewrite the equation 3x + 2y = 5 in slope-intercept form?

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To rewrite the equation 3x + 2y = 5 in slope-intercept form, we first need to understand what slope-intercept form is. The slope-intercept form of a linear equation is given by:

y = mx + b

where:

  • m is the slope of the line,
  • b is the y-intercept (the value of y when x = 0).

Now, let’s start with the original equation:

3x + 2y = 5

The goal is to solve for y in terms of x.

1. First, isolate 2y on one side by subtracting 3x from both sides:

2y = 5 - 3x

2. Next, divide every term by 2 to solve for y:

y = rac{5}{2} - rac{3}{2}x

3. Finally, you can rearrange it to match the slope-intercept form:

y = -rac{3}{2}x + rac{5}{2}

Now, we have the equation in slope-intercept form, which shows us that:

  • The slope (m) is -3/2
  • The y-intercept (b) is 5/2

This means that for every one unit increase in x, y decreases by 3/2 units. The line intersects the y-axis at the point (0, 5/2).

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