What is the linear equation #10y=-6x-9# in standard form?

1 Answer

The equation for a line in standard form, or slope-intercept form, is #y = mx + b#, where #m# is the slope, and #b# is the y-intercept.

To convert the equation #10y = -6x - 9# to standard form, do the following:

  1. Divide both sides of the equation by 10:

    #(10y)/10=-(6x)/10 - 9/10#
    #y=-(6x)/10 - 9/10#

  2. Reduce #-(6x)/(10)# to #-(3x)/(5)#, and you will get the equation in standard form:

    #y = -3/5x - 9/10#.

The slope (#m#) is #-3/5#, and the y-intercept (#b#) is #-9/10#.

Graphically, this is what the function looks like:

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Usually, if the question asks where does a line intersect the y-axis or the y-intercept, it is usually written in terms of a point on a graph where x = 0.
In this equation, the point is #(0,-9/10)#.