Question

Find the intercepts of y=1/3x +1 .

Answer 1

Consider the following function:

`y=(1)/(3)x\text{ +1}`

The intercepts of a graph are points at which the graph crosses the axes. In fact, the x-intercept is the point at which the graph crosses the x-axis. In other words, the x-intercept of this function is when y= 0, that is, when:

`0=(1)/(3)x\text{ +1}`

this is equivalent to:

`(1)/(3)x\text{ = -1}`

Solving for x, we get:

`x\text{ = -3}`

we can conclude that the x-intercept is on the point:

`(x,y)=(-3,0)`

On the other hand, the y-intercept is the point at which the graph crosses the y-axis, that is when x=0. That is, when:

`y=(1)/(3)(0)\text{ +1}`

this is equivalent to:

`y=1`

we can conclude that the y-intercept is on the point:

`(x,y)=(0,1)`

So that, the correct answers are:

the x-intercept is on the point:

`(x,y)=(-3,0)`

the y-intercept is on the point:

`(x,y)=(0,1)`