Question

Write the equation of the line that has an undefined slope and passes through the point (4, 7). User: What is the slope of a line that is parallel to the x-axis? User: What is the slope of the line that passes through the points (-3, 5) and (1, 7)? User: Which of the following equations is the translation 2 units left of the graph of y = |x|?

Answer 1

For the first question we use point-slope form of an equation

y-
`y_(1)`=m(x-
`x_(1)`)
y=m(x-
`x_(1)`)+
`y_(1)`

then we plug in the known values

y=m(x-4)+7

we leave the slope as variable m since it is undefined

For Question 2

A line that is parallel to the x-axis is a horizontal line and since the slope of a line is defined as the Δy/Δx (change in y/change in x) and the change in y is 0 at any 2 points observed on the line the slope is 0. (0/any number is 0)

For Question 3

Following the same relationship as question 2 we can solve for the slope.

Δy/Δx

`y_(1)`-
`y _(2)`/
`x_(1)`-
`x_(2)`

now we plug in the known values from the two points given

(5-7)/(-3-1)
-2/-4
m=1/2 or 0.5

and For the Final Question

a translation left or right is done by affecting the x variable if you add 2 to x then the x value will have to be 2 less to get the same result...in other words when x is 1 the value of y is also 1...but if I wanted the whole equation translated left 2 unites then I would want the same y-value at an x-value 2 smaller... in other words, in our example x will be -1 when y is 1. For this value found on the graph to match the equation our x value must have 2 added to it in the equation....therefore the equation that translates y=|x| two units left is...

y=|x+2|

Answer 2

1.

Answer:

`y = m(x - 4) + 7`

Step-by-step explanation:

as we know that equation of straight line passing through a fixed point and having undefined slope is given as

`y - y_1 = m(x - x_1)`

here we have

`(x_1, y_1) = (4, 7)`

so we will have

`y - 7 = m(x - 4)`

`y = m(x - 4) + 7`

2.

Answer:

slope = ZERO

Step-by-step explanation:

Slope of the straight line is defined as the tangent of the angle made by the line with respect to x axis

here we need to find the slope of a straight line parallel to x axis so the angle is ZERO degree

hence the slope will be given as

`m = tan 0`

`m = 0`

3.

Answer:

`m = 0.5`

Step-by-step explanation:

Slope of a straight line passing through two different points is given as

`m = (y_2 - y_1)/(x_2 - x_1)`

here we will have

`m = (7 - 5)/(1 + 3)`

`m = (2)/(4)`

`m = 0.5`

4.

Answer:

`y = |x - x'|`

here x' = any positive number

Step-by-step explanation:

If we translate the graph 2 units left of the given position so we can say that we have shifted the graph above from its given position.

So we will have

`y = |x - x'|`

here x' = any positive number