Question

the x- intercept is the x-coordinate of the point where a graph crosses the x- axis. what is the slope of a line that has a y- intercept but no x- intercept

Answer 1

Problem 1

Part a) The graph in the attached figure

Part b) see the explanation

Problem 2

The slope of a horizontal line is equal to zero

Explanation:

we have two questions

1) The Viera family is traveling from Philadelphia to Orlando for vacation. the equation y=1,000 - 65 x represents the distance in miles remaining in their trip after x hours

Part a. graph the equation

Part b.interpret the slope and the y-intercept

2) The x- intercept is the x-coordinate of the point where a graph crosses the x- axis. what is the slope of a line that has a y- intercept but no x- intercept

Problem 1)

Part a) Graph the equation

Let

x -----> the time in hours

y ----> the distance in miles

we have

`y=1,000 - 65x`

This is a linear equation (the graph is a line)

To graph the line plot the intercepts and join the points

Find out the y-intercept

The y-intercept is the value of y, when the value of x is equal to zero

For x=0

`y=1,000 - 65(0)=1,000`

The y-intercept is the point (0,1,000)

Find out the x-intercept

The x-intercept is the value of x, when the value of y is equal to zero

For y=0

`0=1,000 - 65x`

`1,000=65x`

`x=15.385`

The x-intercept is the point (15.385,0)

using a graphing tool

Plot the intercepts and join the points to graph the line

see the attached figure

Part b) Interpret the slope and the y-intercept

we have

`y=1,000 - 65x`

This is the equation of a line in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-intercept

In this problem we have

`m=-65(miles)/(hour)`

The slope represent the speed from Philadelphia to Orlando and is negative because is a decreasing function

The y-intercept is the value of y, when the value of x is equal to zero

In this problem

The y-intercept is the distance from Philadelphia to Orlando (1,000 miles) at the beginning of the trip (value of x equal to zero)

Problem 2

we know that

If a line has a y- intercept but no x- intercept, then we have a horizontal line (parallel to to the x-axis)

A horizontal line has only y-intercept

The slope of a horizontal line is equal to zero