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 Question from nell, a student: Find the slope of the line with equation 7-3y=2x

Hi Nell.

The slope of a line can be read from its equation when you re-arrange the equation into "slope-intercept" form, which looks like this example:

y = -8x - 7

In this case the slope (which we often just call "m") is -8. The slope is the value in front of the x, including the minus sign if there is one.

The model for the slope-intercept form is

y = mx + b

where m is the slope and b is the y-intercept. Notice that in my example earlier, the y-intercept is -7. This means that the line intercepts the y axis at y=-7, in other words, it passes through the point (0, -7).

To re-arrange the equation, you just use the usual algebra rules to "solve for y". Here is another example that is close to your question: what is the slope of 15 - 3y = 6x:

15 - 3y = 6x
-3y = 6x - 15
-3y / (-3) = (6x - 15) / (-3)
y = (6x) / (-3) - (15) / (-3)
y = -2x + 5

Now this is in the y = mx + b form, so I can see that the slope is -2.