Respuesta :
Solution:
Consider the following function:
[tex]y=\frac{1}{3}x\text{ +1}[/tex]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:
[tex]0=\frac{1}{3}x\text{ +1}[/tex]this is equivalent to:
[tex]\frac{1}{3}x\text{ = -1}[/tex]Solving for x, we get:
[tex]x\text{ = -3}[/tex]we can conclude that the x-intercept is on the point:
[tex](x,y)=(-3,0)[/tex]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:
[tex]y=\frac{1}{3}(0)\text{ +1}[/tex]this is equivalent to:
[tex]y=1[/tex]we can conclude that the y-intercept is on the point:
[tex](x,y)=(0,1)[/tex]So that, the correct answers are:
the x-intercept is on the point:
[tex](x,y)=(-3,0)[/tex]the y-intercept is on the point:
[tex](x,y)=(0,1)[/tex]