subject: Intercept Of A Line [print this page] Introduction to y intercept of a line: Introduction to y intercept of a line:
Equation of line is of the form aX+bY=c. a line can cut y axis at most 1 time means that y -intercept of a line are 0 or 1.y-intercet of the line is the point where the line cuts the Y-axis. The equation can cut the y-axis 1 time, sometimes it may not cut the y-axis also, so for a given line equation there can be 0 or more number of y-intercepts. Y-intercept of line is represented by (X,Y) coordinates, where x=0 always, since the point lies on y- axis. to find y-intercept of line we plug in 0 in x in given equation. the following diagram shows the y intercept of line.
In the graph shown, A(x) has 1 intercept and B(x) has no y intercept because it is parallel to y- axis. We can say that when the slope of line is not equal to infinity then there exists a y intercept and if it parallel to y axis that is of the slope of line is infinity then we don"t have a y intercept for that line
Examples on Y-intercept of a Line
Ex: 1 find y -intercept of a line 5x+3y=12
step1: plug in x=0 in the given equation
5(0) + 3y =12
3y = 12
y = $frac{12}{3}$
y = 4
Y-intercept is (0,4)
Ex: 2 find y intercept of line x+y=0
step1: plug in x=0 in the given equation
0 + y = 0
y = 0
y intercept for line x + y = 0 is (0,0)
When Y Intercept of a Line Does not Exist
Some lines never cut y axis, means they are parallel to y axis. If the equation of a line is of the form X=C, where C is a constant then for that line y intercept does not exist.
Ex: 1 equation of a line is x=9
Since it is of the form x=c, we don"t have y intercept for line x=9
Introduction to Y intercept equation:
The equation of a line can be written as a x +by = c, this equation can also be represented in another way called as Y intercept equation. The general formula for y intercept equation is y = mx + c , where m is the slope of the line and c is the point where the line cuts the x axis , that is c is also called as y intercept.
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way to convert general equation to y intercept equation.
ax + by =c
by = -ax + c
y=$frac{-a}{b}$ X + $frac{c}{b}$
here $frac{-a}{b}$ is the slope and $frac{c}{b}$ is the y intercept. from the given y intercept equation we can find the y intercept directly and can be written as (0, $frac{c}{b}$).
The vertical line shown in this graph will cross the x-axis at the number given in the equation. For this equation, the x-intercept is .
Notice this line will never cross the y-axis. A vertical line (other than x = 0) will not have a y-intercept. The line x = 0 is another special case since x = 0 is the equation of the y-axis.
Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y.
