Chapter 8.3, Problem 28E

To determine

Does the line slant upward or downward from left to right? Sketch a graph to justify your answer.

Answer to Problem 28E

The line of the graph with given conditions will be slant upwards from left to right.

Explanation of Solution

Given:

For a certain line, the x -intercept is negative and the y -intercept is positive.

Calculation:

We know that the value of y is 0 on the x -axis and the value of x is 0 on the y -axis.

Since we are told that the x -intercept of a line is negative and y -intercept of line is positive, so line will intersect x -axis before intersecting the y -axis.

This means that the values of y will increase as we will move from left to right. That implies that slope of line will be positive. Therefore, the line of the graph with given conditions will be slant upwards from left to right.

Let us say that the x -intercept of our equation is $(-3,0)$ and the y -intercept is $(0,9)$ .

Upon drawing a line through these points, we will get our required graph as shown below:

  

Upon looking at our graph, we can see that the graph of our line is slant upwards from left to right.

Hence proved.