Write equations for the vertical and horizontal lines calculator

Click here to see ALL problems on Equations Question 388527: Write equations for the vertical and horizontal lines passing through the point (9,7) Found 2 solutions by ewatrrr, solver91311: Answer by ewatrrr(24416)     (Show Source): You can put this solution on YOUR website! Hi, equations for the vertical and horizontal lines passing through the point (9,7) x = 9 (blue) and y = 7 Answer by solver91311(24713)     (Show Source): You can put this solution on YOUR website! A vertical line that passes through the point (9,7) will consist of a set of ordered pairs such that the x-coordinate is always 9, ergo: Which is just another way of saying give me the set of all ordered pairs where the x-coordinate is 9 and I don't care what the y-coordinate is. Using similar logic you should be able to handle the horizontal line part of this question. John My calculator said it, I believe it, that settles it

Let's start with horizontal lines because they're a bit easier. We will start by looking at the line y = 2.

You can see that the line goes left to right which makes it a horizontal line. Think about the sun setting on the horizon to help you remember. Formally, a horizontal line is one in which all the y-values for each point are the same. In our line, all the y-coordinates will be 2, no matter what point you choose.

Let's think about how we would write this equation. We know that y = mx + b is the format we need to follow. It's pretty easy to see that the y-intercept is 2. This makes our equation y = mx + 2.

Now the question is what the slope is. Well, let's take two points and try to find the slope. We will use (1, 2) and (3, 2) just to keep things simple. To find the slope, we subtract the y-values (2 - 2) to get 0. Then, we subtract the x-values (3 - 1) to get 2. Divide 0 by 2 because slope is change in y over change in x. When we do this, we get 0 because 0 divided by anything is 0.

This means our equation is now y = 0x + 2. Multiply out 0 and x to get 0. Now we have y = 0 + 2. Simplify this and we have our equation of y = 2.

You do not have to go through this process each time if you don't want to. Just remember that horizontal lines will always be in the form of y = b.

Vertical Lines

Now we will look at the trickier of the two lines. We will examine the graph of x = 4.

You can see that this graph's line goes straight up and down. Formally, a vertical line is one where all the x-values for a line are the same. Take any point on this graph, and its x-coordinate will be 4.

How to Write the Equations of Vertical and Horizontal Lines Through a Given Point

To find the equations of the vertical line and the horizontal line through the point {eq}(a, b) {/eq}, follow the steps below.

Step 1: A horizontal line has one {eq}y {/eq}-value for all values of {eq}x {/eq} in the domain. If this line passes through point {eq}(a, b) {/eq} where {eq}a {/eq} is the {eq}x {/eq}-coordinate and {eq}b {/eq} is the {eq}y {/eq}-coordinate of the point, the horizontal line will have {eq}b {/eq} as the {eq}y {/eq}-value for all {eq}x {/eq}. The equation to represent this horizontal line is {eq}y = b {/eq}.

Step 2: A vertical line has one {eq}x {/eq}-value for all values of {eq}y {/eq}. If this line passes through point {eq}(a, b) {/eq} where {eq}a {/eq} is the {eq}x {/eq}-coordinate and {eq}b {/eq} is the {eq}y {/eq}-coordinate of the point, this vertical line will have {eq}a {/eq} as its {eq}x {/eq} value for all {eq}y {/eq}. The equation to represent this vertical line is {eq}x=a {/eq}.

How to Write the Equations of Vertical and Horizontal Lines Through a Given Point Vocabulary

Horizontal line: A horizontal line is a collection of points whose {eq}y {/eq}-coordinate is the same for any {eq}x {/eq}-coordinate. Another way to think about a horizontal line is a line with a slope of 0. A horizontal line makes no vertical change throughout its domain. If we substitute 0 for the slope in a general slope-intercept form, we get:$$\begin{align} y&= mx + b \\\\ y& =(0)x + b \\\\ y & = b\\\\ \end{align} $$ Therefore, the equation of a horizontal line is given by: $$y = b $$ where {eq}b {/eq} is a real number.

Vertical line: A vertical line is a collection of points whose {eq}x {/eq}-coordinate is the same for any {eq}y {/eq}-coordinate. The equation of a vertical line is given by: $$x = c $$ where {eq}c {/eq} is a real number.

Let's practice writing the equations of vertical and horizontal lines through a given point with the next two examples.

How to Write the Equations of Vertical and Horizontal Lines Through a Given Point: Example 1

Write the equations of the vertical line and the horizontal line through the point (3,6).

Step 1: A horizontal line has one {eq}y {/eq} value for all {eq}x {/eq} in the domain. If this line passes through the point {eq}(3,6) {/eq} where {eq}3 {/eq} is the {eq}x {/eq}-coordinate and {eq}6 {/eq} is the {eq}y {/eq}-coordinate of the point, the horizontal line will have {eq}6 {/eq} as the {eq}y {/eq} value for all values of {eq}x {/eq}. The equation to represent this horizontal line is {eq}y = 6 {/eq}.

Step 2: A vertical line has one {eq}x {/eq} value for all {eq}y {/eq}. If this line passes through the point {eq}(3, 6) {/eq}, this vertical line will have {eq}3 {/eq} as its {eq}x {/eq} value for all values of {eq}y {/eq}. The equation to represent this vertical line is {eq}x=3 {/eq}.

The horizontal line through (3, 6) is y =6, and the vertical line through (3, 6) is x = 3.

How to Write the Equations of Vertical and Horizontal Lines Through a Given Point: Example 2

Write the equations of the vertical line and the horizontal line through the point {eq}(2,-4) {/eq}.

Step 1: A horizontal line has one {eq}y {/eq} value for all {eq}x {/eq} in the domain. If this line passes through the point {eq}(2,-4) {/eq}, the horizontal line will have {eq}-4 {/eq} as the {eq}y {/eq} value for all values of {eq}x {/eq}. The equation to represent this horizontal line is {eq}y = -4 {/eq}.

Step 2: A vertical line has one {eq}x {/eq} value for all {eq}y {/eq}. If this line passes through the point {eq}(2, -4) {/eq}, this vertical line will have {eq}2 {/eq} as its {eq}x {/eq}-value for all values of {eq}y {/eq}. The equation to represent this vertical line is {eq}x=2 {/eq}.

The horizontal line through (2, -4) is y =-4, and the vertical line through (2, 4) is x = 2.

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