Online graphing calculator to calculate the x and y intercepts of a line, from the given co-efficients. Show
Find X, Y Intercepts of a LineEnter the coefficients X + Y = X intercept Y intercept
Online graphing calculator to calculate the x and y intercepts of a line, from the given co-efficients. Code to add this calci to your website Formula:X = (C - BY) / A Y = (C - AX) / B Where A,B,C - coefficients, X,Y - Points Related Article:
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Created by Krishna Nelaturu Reviewed by Rijk de Wet Last updated: Apr 26, 2022 This y-intercept calculator is the perfect tool to calculate the x- and y-intercept of any given line. Additionally, you can use it to find the line equation from its slope and the x- or y-intercept. Finding intercepts of straight lines is a simple process, but it is pretty common to get the basics mixed up. Let's discuss the following basics in this article so that you're always ready:
If you're interested in finding the line equation in different forms, we recommend our popular slope intercept form calculator and point slope form calculator. Slope, intercepts, and the general line equationWe can express the most general form of a straight line in 2-dimensional space as: ax+by+c=0ax + by + c = 0 where:
You can plot this line on a graph sheet if you know at least two points that lie on this line. We define the y-intercept of this line as the point at which it crosses (or intersects) the y-axis. Specifically, it refers to the y-coordinate of this point, although it is also common to call the point itself the y-intercept. Similarly, the line's x-intercept would be the point (or the x-coordinate) where it intersects the x-axis. The slope (or gradient) of a line is the amount of change in yy for a change in xx. You can learn more about the slope of a line using our slope calculator. We can express the slope, y-intercept and x-intercept of any line ax+by+ c=0ax + by + c = 0 using these equations: yc =−c/bxc=−c/am=−a/b\begin{align*} y_c &= - c/b\\ x_c &= - c/a \\ m &= - a/b \end{align*} where:
In the following sections, we'll prove these equations with an example — but first, let's discuss another form of a line equation. Slope-intercept formWe can also express a line equation in terms of its slope and y-intercept: y=mx+cy = mx + c where:
We could rewrite it to include the y-intercept from the start: y=mx+ycy = mx + y_c You'll find this form very useful when formulating most line equations if you can calculate the slope and y-intercept beforehand. How do you find the y-intercept of a line?To find the y-intercept of a line given by
Or, if the line equation is in the slope-intercept form For example, consider a line given by the equation 2x+3y−2=02x + 3y -2 = 0. The y-intercept lies on the intersection of the y-axis (the line defined by x=0x=0) and our line 2x+3 y−2=02x + 3y -2 = 0. So, we insert x=0x=0 in 2 x+3y−2=02x + 3y -2 = 0 to obtain: 2⋅0+3y −2=03y−2=03y =2∴yc=23\begin{align*} 2\cdot 0+ 3y - 2 &= 0\\ 3y - 2 &=0\\ 3y &= 2\\ \therefore y_c &= \frac{2}{3} \end{align*} How do you find the x-intercept of a line?To find the x-intercept of a line given by
These steps are applicable even if the line equation is in slope-intercept form: Again, consider the line 2x+3y−2=02x + 3y -2 = 0. Its x-intercept lies on the intersection point of the x-axis (y=0y=0) and 2x +3y−2=02x + 3y -2 = 0. So, we insert y=0y=0 in 2x+3y−2=02x + 3y -2 = 0 to obtain: 2x+ 3⋅0−2=02x−2=02x =2∴xc=1\begin{align*} 2x + 3 \cdot 0 - 2 &= 0\\ 2x - 2 &=0\\ 2x &= 2\\ \therefore x_c &= 1 \end{align*} The line 2x + 3y - 2 = 0 with its slope and intercepts.How do you find the line equation from its intercepts?To find the line equation from its x-intercept
Once again, let's consider the line 2x+3y−2=02x + 3y -2 = 0 with (1,0) (1,0) x-intercept and (0,23)(0,\frac{2}{3}) y-intercept. Can we find the line equation with just these intercepts? Let's find out.
m=0−231−0 ∴m=−23\qquad\begin{align*} m &= \frac{0-\frac{2}{3}}{1-0}\\ \therefore m &= -\frac{2}{3} \end{align*}
y= −23x+23\qquad y = -\frac{2}{3}x + \frac{2}{3}
How to calculate x- and y-intercepts using this y-intercept calculatorYou can use this y-intercept calculator in three modes:
Our calculator will also present you with a summary of results and a helpful graph in all these modes! Pat yourself on your back for learning something new today! We believe you're ready to explain to others how to find the slope, y-intercept, and x-intercept of a line. FAQWhat is the y-intercept of the line 2x + 3y = -9?
Do all straight lines have a y-intercept?No. Some lines run parallel to the y-axis, and thus don't have a y-intercept. However, every line in two dimensions has at least one intercept, be it x- or y-intercept. General line equation: ax + by + c =0 Average rate of changeBilinear interpolationCatenary curve… 35 more How do you find the x and yPress the "2nd" key then the "Calc" key. This accesses the trace menu. Scroll down to "Zero" and press "Enter." Using the arrow keys, scroll to the left of the X intercept and press "Enter." Scroll to the right of the intercept and press "Enter'" twice. The X intercept will be displayed the bottom of your screen.
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