Answer:
1/3 and (0,1)
Step-by-step explanation:
In a cartesian plane, we can represent a line using a general equation defined in that plane. Given a line with slope [tex]m[/tex] and a point which it passes through [tex]P_1(x_1,y_1)[/tex] it is possible to obtain the equation of the line from the of the slope-intercept form:
[tex]y-y_1=m(x-x_1)[/tex]
Where:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph provided by the problem we can extract the two points we need.
Let:
[tex]P_1=(x_1,y_2)=(0,1)\\P_2=(x_2,y_2)=(-3,0)[/tex]
Thus:
[tex]m=\frac{0-1}{-3-0} =\frac{-1}{-3} =\frac{1}{3}[/tex]
[tex]y-1=\frac{1}{3} (x-0)\\\\y-1=\frac{1}{3} x\\\\y(x)=\frac{1}{3} +1[/tex]
Now that we know the slope and the equation of the graph, we can easily find the y-intercept of the line. Actually you can conclude what is the y-intercept just by looking the graph, as you can see, the line crosses the y-axis at the point (0,1). However, let's find it using the equation that we found. As you may know, the line will cross the y-axis when x=0, so let's evaluate the function for x=0:
[tex]y(0)=\frac{1}{3}(0) +1=0+1=1[/tex]
Therefore, the y-intercept of the line is (0,1).
