Find the slope and y-intercept of 3x-2y=5 y=3x-5 (my answer=(slope 3) (y-intercept -5)3x-2y=5(my answer=(slope 3/2) (y-intercept -3)

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durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

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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.  

3x-2y=5

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

 Manipulate:

3x-2y=5

`therefore -2y= -3x + 5`

`therefore y= (-3x)/-2 + 5/(-2)`

Simplify:

`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

 

 

Sources:
sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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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` .

vaaruni's profile pic

vaaruni | High School Teacher | (Level 1) Salutatorian

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The given equqtion : 3x-2y=5 We know that the form of the equation of a straigjt line is : y = mx + c where 'm' is the slope of the line, 'c' is the y-intercept and (x,y) are any two points on the line. now our task is to express the given equation in the form of y = mx + c The equation : 3x - 2y = 5 => -2y = -3x + 5 => y = (-3x/-2)+ (5/-2) => y = (3/2)x + (-5/2) here 'm' = (3/2) and c or y-intercept =(-5/2) Hence, slope of the line -> 3/2 y-intercept -> -5/2 or -2.5

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