Question

Which of these equations has a y-intercept of 3?y = 3xy = x + 3y + 3 = xy = x - 3

Answer 1

`y=x+3`

Step-by-step explanation

the y-intercept is the point where the line crosses the y-axis.

when having the equation in the form:

`y=mx+b`

it is called, slope-intercept point

where

m is the slope of the line

and b is the y-intercept

hence, to solve this we need to get the slope-intercept form and check the b value

Step 1

a) y=3x

so

`\begin{gathered} y=3x\rightarrow y=mx+b \\ so \\ m=3 \\ b=0 \end{gathered}`

so, the y intercept is 0,

this equation has not y intercept at 3

Step 2

b)y=x+3

so

`\begin{gathered} y=x+3\rightarrow y=mx+b \\ \text{hence} \\ m=1 \\ b=3 \end{gathered}`

b= 3, so

this equation has a y-intercept of 3

Step 3

)y+3=x

so

`\begin{gathered} \text{isolate y } \\ y+3=x \\ y=x-3 \\ so \\ m=1 \\ b=-3 \end{gathered}`

Step 4

d)y=x+3

so

`\begin{gathered} y=x-3\rightarrow y=mx+b \\ \text{hence} \\ m=1 \\ b=-3 \end{gathered}`

b= 3, so

this equation has not a y-intercept of 3

therefore, the answer is

`y=x+3`

I hope this helps you