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 Question from Norma, a student: write equation in slope intercept form and then find the slope and y-intercept of the corresponding line. please show step by step 1). 2x-3y-9=0 and 2). 3x-4y+8=0

Norma,

I'm going to illustrate with a different equation, 4x - 3y = 7.

The slope intercept form of a line is y = mx + b. What I want you to see here is that y appears alone on the left side of the equality sign and the terms on the right side are organized as a number, m, times x plus another number b. The number m is the slope and b is the y-intercept. I want to put 4x - 3y = 7 in the slope intercept form so that I can determine the slope m and the y-intercept b.

4x - 3y = 7

I want only the y-term on the left side so subtract 4x from each side

4x - 3y - 4x = 7 - 4x

which simplifies to

-3y = 7 - 4x

In the slope intercept form the coefficient in front of y is 1 so divide both sides by -3

-3y/(-3) = (7 - 4x)/(-3)

which becomes

y = -7/3 + (4/3) x.

Changing the order of the terms on the right I get

y = (4/3) x - 7/3.

This is now in the slope intercept form and I can see that the slope m is 4/3 and the y-intercept b is -7/3.

Nw try the two equations you have,
Penny

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