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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.
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A point
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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.
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X – Intercept let y=0 then solve for x |
Y – Intercept let x=0 then solve for y |
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Y = -2x + 4 |
Y = -2x + 4 |
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0 = -2x + 4 |
0 = -2(0) + 4 |
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0 – 4 = -2x + 4 – 4 |
Y = 0+4 |
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-4 = -2x |
Y = 4 |
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-4/-2= -2x/2 |
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2x |
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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.
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X – Intercept let y=0 then solve for x |
Y – Intercept let x=0 then solve for y |
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Y = x² -2x -3 |
Y = x² -2x -3 |
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0 = x² -2x -3 |
0 = (0)² -2 (0) -3 |
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0 = (x+1) (X-3) |
= 0 – 0 -3 |
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X1 = -1, X2 = 3 |
Y = -3 |
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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:
