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 \(m\) and a point which it passes through \(P_1(x_1,y_1)\) it is possible to obtain the equation of the line from the of the slope-intercept form:
\(y-y_1=m(x-x_1)\)
Where:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
From the graph provided by the problem we can extract the two points we need.
Let:
\(P_1=(x_1,y_2)=(0,1)\\P_2=(x_2,y_2)=(-3,0)\)
Thus:
\(m=\frac{0-1}{-3-0} =\frac{-1}{-3} =\frac{1}{3}\)
\(y-1=\frac{1}{3} (x-0)\\\\y-1=\frac{1}{3} x\\\\y(x)=\frac{1}{3} +1\)
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:
\(y(0)=\frac{1}{3}(0) +1=0+1=1\)
Therefore, the y-intercept of the line is (0,1).
