# Give the slope and y-intercept for the equation: y=3x-2

#### cskinner

##### New member
Give the slope and y-intercept for the equation: y=3x-2

#### ChandrikaP

##### New member
Give the slope and y-intercept for the equation: y=3x-2

Y=3x-2

y intercept means where x=0
put x=0 in the equation

y=3(0)-2
Y=-2

Ax + By + C=0

Then the slope of the line is:

slope = m = -A/B

And the y-intercept is:

y-intercept = b = -C/B

so in this equation y=3x-2

c=-2
b=1

slope=2/1
slope=2

#### mmm4444bot

##### Super Moderator
Staff member
y=3x-2

y intercept means where x=0
put x=0 in the equation

y=3(0)-2
y=-2

Ax + By + C=0

Then the slope of the line is:

slope = m = -A/B

And the y-intercept is:

y-intercept = b = -C/B
You're correct, up to this point.

(I changed symbols Y above to y; it's best to use just one symbol.)

so in this equation y=3x-2

c=-2 C=2; it becomes -2 on the right, after subtracting it from each side.

b=1 That ought to say B=1. You're mixing up your symbols B (coefficient) and b (y-intercept)

-C/B = -2/1 so b = -2

slope=2/1 2 is not the correct value in -A/B
slope=2
Remember, A=-3, B=1, C=2

-3x + y + 2 = 0 :cool:

#### mmm4444bot

##### Super Moderator
Staff member
Give the slope and y-intercept for the equation: y=3x-2
Hi. It's easy to answer, if you've learned this special form:

Slope-Intercept Form

Have you seen it? Google "slope intercept form", or look it up in your textbook's index. You'll learn that the equation y=3x-2 is written in Slope-Intercept Form because the two numbers shown are the slope and the y-intercept.

If you're not sure what "slope" or "y-intercept" mean, then you ought to learn those names first.

Let us know, if you have any questions about what you read in your textbook or see in online lessons. :cool:

#### Bronn

##### Junior Member
Y=3x-2

y intercept means where x=0
put x=0 in the equation

y=3(0)-2
Y=-2

Ax + By + C=0

Then the slope of the line is:

slope = m = -A/B

And the y-intercept is:

y-intercept = b = -C/B

so in this equation y=3x-2

c=-2
b=1

slope=2/1
slope=2

Im confused, i thought in slope intercept form the 3x would be the slope. But you're saying its 2?

#### Harry_the_cat

##### Senior Member
Im confused, i thought in slope intercept form the 3x would be the slope. But you're saying its 2?
y=mx +b is in slope intercept form where slope = m and y-int=b.
You are correct (almost). Slope =3 in your question (not 3x just 3).

#### ChandrikaP

##### New member
Im confused, i thought in slope intercept form the 3x would be the slope. But you're saying its 2?

Hi Bronn,

first of all sorry i solved it wrong as i just put those values in y intercept equation,
Ax+By+C=0

Y=3X-2
3X-Y-2=0
m(slope)=-A/B
A=3,B=-1
here A=-(-3)/1
slope=3

#### sean

##### New member
Give the slope and y-intercept for the equation: y=3x-2

y=mx + c

m=slope

Therefore slope = 3

y-intercept is where it cuts the x- axis (when y=0)

Therefore 0=3x-2 ===> 2=3x ===> 2/3=x when y=0 i.e. (2/3,0) is the point at which it cuts the x-axis

#### Harry_the_cat

##### Senior Member
Give the slope and y-intercept for the equation: y=3x-2

y=mx + c

m=slope

Therefore slope = 3

y-intercept is where it cuts the x- axis (when y=0) ...ummm NO! It is called the y-intercept because that is where it cuts the y-axis not the x-axis!!

Therefore 0=3x-2 ===> 2=3x ===> 2/3=x when y=0 i.e. (2/3,0) is the point at which it cuts the x-axis
see comment in red

#### Bronn

##### Junior Member
Hi Bronn,

first of all sorry i solved it wrong as i just put those values in y intercept equation,
Ax+By+C=0

Y=3X-2
3X-Y-2=0
m(slope)=-A/B
A=3,B=-1
here A=-(-3)/1
slope=3
I may aswell ask here. Ive just been learning this stuff. Ive been confused what the C represents. I get that M is slope, the ab and xy are coordinates right? but what does the C represent?

#### Harry_the_cat

##### Senior Member
I may aswell ask here. Ive just been learning this stuff. Ive been confused what the C represents. I get that M is slope, the ab and xy are coordinates right? but what does the C represent?
Hi Bronn,
There are basically two forms of the equation of a straight line.

1. Gradient intercept form: $$\displaystyle y = mx+c$$. This form always starts with $$\displaystyle y=$$. The gradient is m (the coefficient of x) and the y-intercept is c (constant term).
In this form it is easy to just pick out the gradient and y-intercept. Hence the name.

2. Standard form: $$\displaystyle Ax + By +C = 0$$
This form can be rearranged into gradient-intercept form in the following way:

$$\displaystyle Ax + By + C =0$$

$$\displaystyle By= -Ax - C$$

$$\displaystyle y=\frac{-A}{B}x - \frac{C}{B}$$

So the gradient (the coefficient of x) = $$\displaystyle \frac{-A}{B}$$ and the y-intercept is $$\displaystyle \frac{-C}{B}$$.

Note that the c's mean different things. That's why one is usually lower case and one upper case.

the ab and xy are coordinates right?
(x, y) represents points on the line and are the variables. A and B and C OR m and c are constants for a particular line.

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#### Bronn

##### Junior Member
Hi Bronn,
There are basically two forms of the equation of a straight line.

1. Gradient intercept form: $$\displaystyle y = mx+c$$. This form always starts with $$\displaystyle y=$$. The gradient is m (the coefficient of x) and the y-intercept is c (constant term).
In this form it is easy to just pick out the gradient and y-intercept. Hence the name.

2. Standard form: $$\displaystyle Ax + By +C = 0$$
This form can be rearranged into gradient-intercept form in the following way:

$$\displaystyle Ax + By + C =0$$

$$\displaystyle By= -Ax - C$$

$$\displaystyle y=\frac{-A}{B}x - \frac{C}{B}$$

So the gradient (the coefficient of x) = $$\displaystyle \frac{-A}{B}$$ and the y-intercept is $$\displaystyle \frac{-C}{B}$$.

Note that the c's mean different things. That's why one is usually lower case and one upper case.

(x, y) represents points on the line and are the variables. A and B and C OR m and c are constants for a particular line.
so the A and B are constants in standard form, not the same as the (a,b) in point slope form? i.e. (y-b) = m(x-a)
this could get confusing for me..

edit: after clicking the point slope link above, i see maybe using (a,b) in point slope form is a kahn academy thing

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