Question

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

Answer 1

Solution:

Consider the following function:

$y=\frac{1}{3}x\text{ +1}$

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:

$0=\frac{1}{3}x\text{ +1}$

this is equivalent to:

$\frac{1}{3}x\text{ = -1}$

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:

$y=\frac{1}{3}(0)\text{ +1}$

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:

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