<< Chapter < Page Chapter >> Page >

Given m = 4 , find the equation of the line in slope-intercept form passing through the point ( 2 , 5 ) .

y = 4 x −3

Got questions? Get instant answers now!

Finding the equation of a line passing through two given points

Find the equation of the line passing through the points ( 3 , 4 ) and ( 0 , −3 ) . Write the final equation in slope-intercept form.

First, we calculate the slope using the slope formula and two points.

m = −3 4 0 3 = 7 3 = 7 3

Next, we use the point-slope formula with the slope of 7 3 , and either point. Let’s pick the point ( 3 , 4 ) for ( x 1 , y 1 ) .

y 4 = 7 3 ( x 3 ) y 4 = 7 3 x 7 Distribute the  7 3 . y = 7 3 x 3

In slope-intercept form, the equation is written as y = 7 3 x 3.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Standard form of a line

Another way that we can represent the equation of a line is in standard form . Standard form is given as

A x + B y = C

where A , B , and C are integers. The x- and y- terms are on one side of the equal sign and the constant term is on the other side.

Finding the equation of a line and writing it in standard form

Find the equation of the line with m = −6 and passing through the point ( 1 4 , −2 ) . Write the equation in standard form.

We begin using the point-slope formula.

y ( −2 ) = −6 ( x 1 4 ) y + 2 = −6 x + 3 2

From here, we multiply through by 2, as no fractions are permitted in standard form, and then move both variables to the left aside of the equal sign and move the constants to the right.

2 ( y + 2 ) = ( −6 x + 3 2 ) 2 2 y + 4 = −12 x + 3 12 x + 2 y = −1

This equation is now written in standard form.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the equation of the line in standard form with slope m = 1 3 and passing through the point ( 1 , 1 3 ) .

x + 3 y = 2

Got questions? Get instant answers now!

Vertical and horizontal lines

The equations of vertical and horizontal lines do not require any of the preceding formulas, although we can use the formulas to prove that the equations are correct. The equation of a vertical line is given as

x = c

where c is a constant. The slope of a vertical line is undefined, and regardless of the y- value of any point on the line, the x- coordinate of the point will be c .

Suppose that we want to find the equation of a line containing the following points: ( −3 , −5 ) , ( −3 , 1 ) , ( −3 , 3 ) , and ( −3 , 5 ) . First, we will find the slope.

m = 5 3 3 ( −3 ) = 2 0

Zero in the denominator means that the slope is undefined and, therefore, we cannot use the point-slope formula. However, we can plot the points. Notice that all of the x- coordinates are the same and we find a vertical line through x = −3. See [link] .

The equation of a horizontal line is given as

y = c

where c is a constant. The slope of a horizontal line is zero, and for any x- value of a point on the line, the y- coordinate will be c .

Suppose we want to find the equation of a line that contains the following set of points: ( −2 , −2 ) , ( 0 , −2 ) , ( 3 , −2 ) , and ( 5 , −2 ) . We can use the point-slope formula. First, we find the slope using any two points on the line.

m = −2 ( −2 ) 0 ( −2 ) = 0 2 = 0

Use any point for ( x 1 , y 1 ) in the formula, or use the y -intercept.

y ( −2 ) = 0 ( x 3 ) y + 2 = 0 y = −2

The graph is a horizontal line through y = −2. Notice that all of the y- coordinates are the same. See [link] .

Coordinate plane with the x-axis ranging from negative 7 to 4 and the y-axis ranging from negative 4 to 4.  The function y = negative 2 and the line x = negative 3 are plotted.
The line x = −3 is a vertical line. The line y = −2 is a horizontal line.

Finding the equation of a line passing through the given points

Find the equation of the line passing through the given points: ( 1 , −3 ) and ( 1 , 4 ) .

The x- coordinate of both points is 1. Therefore, we have a vertical line, x = 1.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
v=lbh calculate the volume if i.l=5cm, b=2cm ,h=3cm
Haidar Reply
Need help with math
Peya
can you help me on this topic of Geometry if l help you
litshani
( cosec Q _ cot Q ) whole spuare = 1_cosQ / 1+cosQ
Aarav Reply
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?
Maxwell Reply
the indicated sum of a sequence is known as
Arku Reply
how do I attempted a trig number as a starter
Tumwe Reply
cos 18 ____ sin 72 evaluate
Het Reply
Practice Key Terms 7

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask