Question

What is the slope and y-intercept of line q graphed below?

Answer 1

The third option is the right one

Answer 2

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).