Question

A line has a slope of 2 and a y-intercept of 0 what is its equation in slope intercept form

Answer 1

Answer:

y = 2x

Step-by-step explanation:

Answer 2

Explanation:

Slope-intercept form is given by  

y

=

m

x

+

b

, where  

m

is the slope of the line and  

b

is the  

y

-intercept of the line, or the value of  

y

where the line crosses the  

y

-axis.

Given that the slope of the line is  

2

, we have  

m

=

2

, and because the line crosses the  

y

-axis at the point  

(

0

,

0

)

, where  

y

=

0

and  

x

−

0

, we have:

y

=

2

x

+

0

Or, equivalently,  

y

=

2

x

If the point given were not the origin, you could use  

y

=

m

x

+

b

to find  

b

by plugging the  

x

and  

y

value of the point in for  

x

and  

y

in the equation along with the given slope  

m

and solving for  

b

.

Given  

m

=

2

and  

(

x

,

y

)

=

(

0

,

0

)

:

0

=

2

(

0

)

+

b

⇒

0

=

b

We would then put this value back into  

y

=

m

x

+

b

for  

b

, along with the slope  

m

, yielding the same answer as above:  

y

=

2

x

.