Finding Intercepts From an Equation

Equation of a Line Passing Through Two Points

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.


X – Intercept

let y=0 then solve for x

Y – Intercept

let x=0 then solve for y

Y = -2x + 4

Y = -2x + 4

0 = -2x + 4

0 = -2(0) + 4

0 – 4 = -2x + 4 - 4 

Y = 0+4

-4 = -2x

Y = 4

-4/-2= -2x/2

 

2x

 

Written as point; (2,0)

Written as point; (0,4)


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.


X – Intercept

let y=0 then solve for x

Y – Intercept

let x=0 then solve for y

Y = x² -2x -3

Y = x² -2x -3

0 = x² -2x -3

0 = (0)² -2 (0) -3

0 = (x+1) (X-3)

= 0 – 0 -3

X1 = -1, X2 = 3

Y = -3

as points; (-1,0) and (3,0)

as points; (0,-3)


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:

FAQs (Frequently Asked Questions)

Q1. What is Meant by the Slope Form of a Line?

Answer: Slope-Intercept Form of the Equation of a Line typically refers to a linear equation expressed in the form. y = m x + b {y = mx + b} y=mx+b is in slope-intercept form where: m represents the slope, while b represents the y-intercept.


Moreover, in order to find the slope-intercept form of a line, we write an equation in the form of slope-intercept, given a graph of that equation, select two points on the line and use them to determine the slope. This is said to be the value of m in the equation. Next, we will find the coordinates of the y-intercept form, this must be of the form (0, b). The y- coordinate is said to be the value of b in the equation.

Q2. What is Meant by X-intercepts and Y-intercepts?

Answer:  The intercepts are marked graphically which are actually the points at which the graph passes through the axes. That being said, the x-intercept is the point where the x-axis passes through the x-axis. At this point, the value of y-coordinate is zero. In the same manner, The y-intercept is the point where the graph passes through the y-axis. At this point, the value of x-coordinate is zero. Moreover, in order to determine the x-intercept, we are required to set y equal to zero (y=0) and solve for x. Likewise, to find out the y-intercept, we have to establish x equal to zero (x=0) and solve for y.