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:

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

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

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:

$m = 0.5$

Explanation:

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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

here we will have

$m = \frac{7 - 5}{1 + 3}$

$m = \frac{2}{4}$

$m = 0.5$

4.

Answer:

$y = |x - x'|$

here x' = any positive number

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