Chapter 3, Problem 1MCP

In Exercises 1−3, use each graph to determine

a. the x-intercept, or state that there is no x-intercept.

b. the y-intercept, or state that there is no y-intercept.

c. the line’s slope, or state that the slope is undefined.

1.

To determine

(a)

The x -intercept of the given graph.

Answer to Problem 1MCP

Solution:

The x -intercept is 4.

Explanation of Solution

Given:

The graph of the line.

Concept used:

To find the x -intercept of a given line on a graph, the point where the line is intersecting the x - axis is the x -intercept and the point where the line is intersecting the y axis is the y -intercept.

Calculation:

From the given graph, we observe that the line is intersecting x - axis at $x=4$. Therefore, the x- intercept of the line is at $(4,0)$.

Conclusion:

Therefore, the x -intercept of the graph is 4.

To determine

(b)

The y -intercept in the graph given below.

Answer to Problem 1MCP

Solution:

y -intercept is 2.

Explanation of Solution

Given:

The graph of the line.

Concept used:

To find the x -intercept of a given line on a graph, the point where the line is intersecting the x - axis is the x -intercept and the point where the line is intersecting the y axis is the y -intercept.

Calculation:

The line is intersecting y - axis at 2, which makes it the y -intercept.

Conclusion:

Therefore, the y -intercept of the given line is 2.

To determine

(c)

The slope of the line given in the graph.

Answer to Problem 1MCP

Solution:

The line's slope is: $-\frac{1}{2}$

Explanation of Solution

Concept used:

Follow the below process for find the slope the given line:

Pick two points on the line and determine their coordinates.

Determine rise: the difference in y -coordinates of these two points.

Determine run: the difference in x -coordinates for these two points.

Divide the difference in y -coordinates by the difference in x -coordinates (rise/run or slope).

Calculation:

For slope, consider the two points $(0,2)$ and $(4,0)$ on the graph.

Difference in y -coordinates for these two points $(0,2)$ and $(4,0)$ : $2-0=2$.

Difference in x -coordinates for these two points $(0,2)$ and $(4,0)$ : $0-4=-4$.

Now, divide the difference in y -coordinates by the difference in x -coordinates and get,

   $\begin{array}{c}\frac{2-0}{0-4}=-\frac{2}{4}\\ =-\frac{1}{2}\end{array}$

Conclusion:

Therefore, the slope of the graph is $-\frac{1}{2}$.