Finding Intercepts From an Equation

The general form equation of a line connecting two points (x₁, y₁) and (x₂, y₂) is given as y – y₁={[y₂ - y₁]/[x₂ - x₁]} * (x - x₁). The slope form of a line connecting two points (x₁, y₁) and (x₂, y₂) is equivalent to {y₂ - y₁}/{x₂ - x₁}. Remember that anytime we need to obtain the equation of a line or equation of a line in standard form, we require two things i.e.

1. A point       

2. A slope

Intercepts Y

The y-intercepts are actually the points where the graph of a function or an equation “touches” or passes through the y-axis in the Cartesian Plane. You may also consider this as a point having x-value of zero.

In order to determine the y-intercepts of an equation, let x = 0, then solve for y.

In a point notation, it is expressed as (0,y)

How to Find the X-Intercepts

Just like the y-intercept, the x-intercepts are basically the points where the graph of a function or an equation “touches” or passes through the x-axis of the Cartesian Plane. Imagine this as a point with y-value of zero.

In order to find the x-intercepts of an equation, let y = 0, then solve for x.

In a point notation, it is expressed as (x, 0).

Finding Intercepts Equation

Let’s first learn how to Find the x and y-intercepts of the general form equation of a line y = –2x + 4.

In order to identify the x-intercepts algebraically, we let y=0 in the equation and then solve for x. Likewise, to find the intercept y algebraically, we let x=0 in the equation and then solve for values of y.

Below is the graph to verify our answers are correct.

How to Find the X and Y-Intercepts of the Quadratic Equation

Let's learn how to determine x and y-intercepts of the quadratic equation. Consider a quadratic equation: y = x² − 2x − 3.

Now, the graph of this quadratic equation will be in the shape of a parabola. We assume it to have a “U” shape in which it would either open up or down.

In order to solve for the x-intercept of this problem, we would require factoring a simple trinomial. Then you set each binomial factor equivalent to zero and solve for value of x.

Below are our solved values for both x and y-intercepts that match along with the graphical solution.

Solved Examples

Example:

Find the intercept of the given function

Determine the intercepts of the equation given as; y=-3x - 4. Then plot the graph with the help of only the intercepts.

Solution:

Set y=0 in order to find out the x-intercept.

y=−3x−4

0=−3x−4

4=−3x

-4/3 = x

= (−4/3) = 0 x intercept

Set y=0 in order to find out the y-intercept.

y=−3x−4

y=−3x(0)−4

y= -4

4=−3x

-4/3 = x

=(0, -4)y intercept

Now, let’s plot both x and y intercept slope intercept form, and draw a line crossing through them as in the figure shown below: