How do you determine the slope of the line represented by the equation 6x + 8y = 12?

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To find the slope of the line given by the equation 6x + 8y = 12, we first need to get it into the slope-intercept form, which is y = mx + b, where m stands for the slope and b represents the y-intercept.

Here’s a step-by-step guide:

  1. Start with the original equation:

    2. 6x + 8y = 12

  2. Isolate the y term:

    3. Subtract 6x from both sides:

    8y = 12 – 6x

  1. Simplify:

    2. Now, we will rearrange it to make it look more like slope-intercept form:

    8y = -6x + 12

  1. Divide by 8:

    2. To solve for y, divide each term by 8:

    y = –6/8x + 12/8

This reduces to:

y = –3/4x + 3/2

By writing the equation in slope-intercept form, we can see that the slope (m) of the line is -3/4.

In summary:

The slope of the line represented by the equation 6x + 8y = 12 is -3/4.

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