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I will answer the less obvious of your 2 choices as the eNotes rules do not allow multiple questions. You have stated the slope and I will show you how to find the y-intercept. Apply your understanding from this question to check the correctness of your other answers or post the questions separately.
The standard form of the linear (straight line ) equation is
y = mx+ c (some will use y = mx + b which is the same)
m=the gradient or slope and c= the y-intercept
`therefore -2y= -3x + 5`
`therefore y= (-3x)/-2 + 5/(-2)`
`therefore y= (3x)/2 - 5/2`
Now, if y=mx+c you can identify the slope and the y-intercept:
`therefore ` y intercept = -5/2
You need to remember that you may write the equation of a line in different forms and slope intercept form `y = mx + b` is one of them, hence, you need to convert the given equation `3x - 2y = 5` to the slope intercept form.
You need first isolate the term that contain `y` to the left side, moving all the rest of terms to the right, such that:
`-2y = -3x + 5`
Notice that the movement of a term from one side to the other implies the change of the sign, hence, since `3x` was positive to the left, it will become negative to the right.
You need to divide the equation by `-2` such that:
`y = (-3)/(-2)*x + 5/(-2) => y = (3/2)x - 5/2`
You need to identify the coefficients m and b such that:
`m = 3/2` and `b = -5/2`
You need to remember that m represents the slope of the line and b represents y intercept.
Hence, evaluating the slope and the y intercept of the given line yields `m = 3/2` and `b = -5/2` .
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