Calculating the x- and y-intercepts of any given line is made simple with the help of this y-intercept calculator. The line equation can also be determined using the slope and x- or y-intercept of the line.
Although finding intercepts of straight lines is a simple process, it is rather typical to confuse the fundamentals. So that you’re always prepared, let’s go over the following fundamentals in this article:
Table of Contents
The General Line Equation, Intercepts, and Slope
In two dimensions, a straight line can be expressed in the following ways:
The formula is ( ax + by + c = 0 )
where:
- The constant term is denoted by c
- The variables x and y stand in for the two dimensions.
- The coefficients of the x and y terms are denoted by a and b, respectively.
If you know at least two points that lie on this line, you can plot this line on graph paper. The location of this line’s y-intercept is where it crosses (or intersects) the y-axis. Although the point itself is also frequently referred to as the y-intercept, this phrase specifically refers to the y-coordinate of this point. The location (or x-coordinate) where a line meets an axis is known as its x-intercept.
The amount that yy changes as xx changes are known as the slope (or gradient) of a line. Use our slope calculator to find out more about a line’s slope. We can write any line’s slope, y-intercept, and x-intercept as
( ax + by + c = 0 ) using the following formulas:
Start by aligning y c, then x c, then m, then a/b, and finally end by aligning y c.
yc = – c/b
cc = – c/a
m = -a/b
~where:
The line’s yc-intercept, xc-intercept, and slope are all represented by the symbols m , respectively.
In the sections that follow, we’ll use an example to explain these equations, but first, let’s talk about another type of line equation.
Slope-intercept Pattern
~ The slope and y-intercept of a line equation can also be used to express it:
- y = mx+c
~ where
- m represents the line’s slope, and c its y-intercept so that c = y ( c = yc )
We might modify it from the beginning to integrate the y-intercept:
- y = MX + yc
If you know the slope and y-intercept in advance, you’ll find this form to be quite helpful when formulating the majority of line equations.
How can I Calculate A Line’s Y-intercept?
These easy techniques can be used to determine the y-intercept of a line with the equation ( ax + by + c = 0 )
•To obtain by + c = 0, replace the line equation with the value x = 0.
•By rearranging this equation, you may determine the y-intercept, where yc = c/b.
•Utilize the y-intercept calculator to validate your findings.
- Even if the line equation is in slope-intercept form, y = MX + c, you can still follow these procedures to get xc = c/m.
Consider once more the equation 2x + 3y -2 = 0. Its x-intercept is located at the location where the x-axis (x=0) and 2x + 3y -2 = 0 connect. Thus, by adding x=0 to 2x + 3y -2 = 0, the following is obtained:
2 • 0+3y−2 = 0
3y–2 = 0
3y = 2
.°. Yc = 2/3
From The Line’s Intercepts, How do You Obtain The Line Equation?
The line equation can be found by using the x-intercept of a line given by ax + by + c = 0, follow these simple steps:
- M = (0 yds)/(xc 0) yields m = yc/xc, which is the slope of the line.
Considering that c = yc, write the line equation as y = MX + c in the slope-intercept form.
Use the equation as is, or simplify and rearrange it as necessary.
Let’s take a look at line 2x + 3y -2 = 0 x-intercept lies on the intersection point of the x-axis (y=0) and 2x + 3y -2 = 0. So, we insert y=0 in 2x + 3y -2 = 0 to obtain:
2x + 3 • 0 – 2 = 0
2x – 2 = 0
2x = 2
xc = 1
Let’s take a look at line 2x + 3y -2 = 0 with ( 1, 0 ) x-intercepts and ( 0 ,⅔ ) y-intercepts. Find out now.
- We can determine the slope mm of this line using these two intercept points:
m = 0 – ⅔
-———
1 – 0
m = – ⅔
- Formulate the line equation in the slope-intercept form y = mx + c
Y = – ⅔ x + ⅔
- The result of simplifying and rearranging this equation is 2x + 3y – 2 =0.
Using This Y-intercept Calculator, Determine The X- And Y-intercepts
There are three ways to use this y-intercept calculator:
- From The Line’s General Equation, Determine The X- And Y-Intercepts As Well As The Slope
Select the “Line equation is axed by c = 0” mode. You can use the calculator to get all the answers by entering the values for a, b, and c.
- To Determine A Line’s Slope, Y-Intercept, and X-Intercept from Its Slope-Intercept Form
Select the “Y = MX + c Line Equation” mode.
m and c’s values should be entered.
•The calculator will handle the rest while you sit back and unwind
- Use The Mode “Line Equation is to be Mb Determined” To Discover An Equation That has The Specified Intercepts
- The x-intercept and y-intercept values should be entered.
- The findings are precise and timely, so enjoy.
- In each of these modes, our calculator will also provide you with a summary of the results and a useful graph!
Conclusion
So here we discussed how to find y-intercept lines by using the y-intercept calculator. Congratulate yourself on today’s new knowledge! We believe you are now capable of describing to others how to determine a line’s slope, y-intercept, and x-intercept.
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