What Are The X Intercepts

In Maths, an intercept is a betoken on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line , y = mx+c, where m is slope and c is the y-intercept.

There are basically two intercepts, ten-intercept and y-intercept. The signal where the line crosses the ten-axis is the x-intercept and the betoken where the line crosses the y-centrality is the y-intercept. In this article, yous volition learn what is the intercept, how to notice the intercept for a given line, graphing intercepts along with solved examples.

Definition of Intercept

The bespeak where the line or curve crosses the axis of the graph is called intercept. If a bespeak crosses the ten-axis, then it is called the x-intercept. If a point crosses the y-axis, then information technology is chosen the y-intercept.

The pregnant of intercept of a line is the point at which it intersects either the x-axis or y-axis. If the centrality is not specified, usually the y-axis is considered. It is normally denoted by the letter ' b' .

Except that line is accurately vertical, it will constantly cross the y-axis somewhere, fifty-fifty if it is way off the elevation or bottom of the chart.

Also read: Equation of plane in intercept class

Intercept Formula

The equation of the line, which intersects the y-axis at a point is given by:
y = mx + c
Now, nosotros have to write the intercept grade of the line, we can replace c with b. Thus, the equation becomes:

y = mx + b
Hence, the formula for the y-intercept of a line is given by:
b = y – mx
Where, b is the intercept, one thousand is the slope of the line and y and ten indicate the points on the y-axis and x-axis respectively.

Now, another way of writing the equation of the line, considering a line is intersecting the 10-axis and y-axis at signal a and b respectively.
x/a + y/b = ane
Hither, a and b are the intercepts of the line which intersect the x-centrality and y-centrality, respectively. The values of a and b can be positive, negative or zero and explain the position of the points at which the line cuts both axes, relative to the origin.

How to Observe X and Y Intercepts?

Consider a straight line equation Ax + By = C.

Dissever the equation by C,

(Ax/C) + (By/C) = C/C

[x/(C/A)] + [y/(C/B)] = 1

Comparison this equation with the equation of a line in intercept course, (x/a) + (y/b) = one,

Nosotros get, x-intercept = a = C/A

y-intercept = b = B/C

Alternatively,

To find the ten-intercept, substitute y = 0 and solve for x.

i.due east. Ax + B(0) = C

Ax = C

x = C/A

To find the y-intercept, substitute x =0 and solve for y.

i.e. A(0) + By = C

By = C

y = C/B

Get through the example given below to sympathise this concept in a improve mode.

Example: Let u.s. assume the straight-line equation 5x +2y =ten

To find x-intercept:

Substitute y=0 in the given equation

5x + 2(0) = x

5x =ten

x =2

To find y-intercept

Substitute ten =0 in the given equation

v(0) + 2y =x

2y = 10

y = 5

Therefore, 10 -intercept is (2, 0)

y -intercept is (0, v)

Two Indicate Form

The formula of the line formed by the 2 points is given past:

y-y₁/y₂-y_i = x-ten₁/x_two-x_one

Intercept Form

Say, P(a, 0) = (x_one, y₁) and Q(0, b) = (x_ii, y_ii) are the two points of the line which cuts the x-axis and y-centrality, relative to the origin(0,0). Then the formula becomes:

=> y – 0 / b – 0 = x – a/ 0 – a

=> y/b = x/-a – a/-a

=> 10/a + y/b = one

Hence, proved.

Learn more nearly the two-point form here.

Slope Intercept Form

The equation of the line making an intercept c on the y-axis and having slope yard is given by:

y = mx + c

Note: The value of c could be positive or negative since the intercept is fatigued on the positive or negative side of the y-axis, respectively.

Also, check: Slope intercept class

Intercept Graph

The intercepts are the points on a graph at which the graph crosses the ii axes (x-axis and y-axis). The betoken where the graph crosses the x-axis is called the x-coordinate and the point where the graph crosses the y-axis is chosen the y-coordinate.

Intercept Graph

In the above intercept graph, where a line L makes x-intercept a and y-intercept b on the axes.

Thus, the equation of the line making intercepts a and b on the x-and y-axis, respectively, is:

x/a + y/b = 1

Solved Examples

Example 1: Let two intercepts P(2,0) and Q(0,three) intersect the ten-centrality and y-axis, respectively. Find the equation of the line.

Solution: Given, 2 intercepts P(2,0) and Q(0,three) intersect the x-axis and y-axis.

From the equation of the line we know,

10/a + y/b = 1 ……….. (1)

Here, a = 2 and b = three

Therefore, putting the values of intercepts a and b, in equation ane, we get:

=>x/2 + y/3 = 1

=> 3x + 2y = six

=> 3x + 2y – 6 = 0,

Therefore, the equation of the line is 3x + 2y – vi = 0.

Example ii: Find the equation of the line, which makes intercepts –3 and two on the x- and y-axes respectively.

Solution: Given, a = –3 and b = 2.

By intercept form, we know that;

ten/a + y/b = 1

x/-3 + y/ii = ane

2x – 3y + 6 = 0.

Hence, this is the required equation.

Example 3: A line passes through P (1, ii) such that its intercept between the axes is bisected at P. What is the equation of the line?

Solution: The equation of a line making intercepts a and b with x-axis and y-axis, respectively, is given by:

10/a + y/b = 1

one = (a+0)/two ⇒ a = 2

2 = (0 + b)/2 ⇒ b = iv

Therefore, the required equation of line is;

10/2 + y/four = 1

⇒ 2x + y – 4 = 0

Practice Issues

Find the 10-intercept and y-intercept for the line 5x – 8y = 2.
If the y-intercept of a line is -four and the slope is two/3, then write its equation.
What is the equation of a line whose x and y-intercepts are given as 1/3 and -three?

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Frequently Asked Questions – FAQs

What is an intercept in Maths?

An intercept is a bespeak where the directly line or a curve intersects the y-axis in a aeroplane. It is as well said to be a y-intercept.

What is the formula for y-intercept?

The formula for y-intercept is given by:
b = y – mx
Where b is the y-intercept and g is the gradient of the line

What is the equation of the line with respect to x and y-intercepts?

The equation of the line, when a line is intersecting the x-axis and y-axis at point a and b respectively is given by:
x/a + y/b = 1

If a line intersects the y-axis at a indicate, then what is the value of 10-coordinate?

If a line intersects the y-axis at a point, the value of the x-coordinate will exist equal to nada.

What is the gradient formula?