What is the Formula to Find X Intercept?
The x-intercepts of a function can be also known as the function's zeros. Take a look at the function y = f. (x). We are already aware of:
The x-intercept(s) is(are) the point(s) on the graph where it intersects the x-axis.
The y-coordinate of a point on the x-axis is 0.
To find the x-intercept of a function, simply substitute y = 0 in its equation and solve for x value (s).
How to Find the X Intercept of a Line?
Let's look at how to find the x intercept and the x intercept formula. An x-intercept is a point in analytic geometry where the graph of a function or relation intersects with the x-axis of the coordinate system, using the common convention that the horizontal axis represents a variable x, as well as the vertical axis, represents a variable y.
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A line Ax + By = C's X-Intercept Formula is x = c/a.
A line's X-Intercept Formula in the slope-intercept form y = mx + c is x = -c/m.
In which case, The slope of the line is denoted by m.
The intercept of the line is denoted by c.
The point-slope form of a line's X-intercept Formula is y – b = m(x – a).
x = b/m - a
In which case, The slope of the line is denoted by m. (a, b) represents a point on the line.
Solved Questions
Question 1) Find the x-intercept of the function y = x2 - 7x + 10.
Solution:
To find: The x-intercept of the function y equals x2 - 7x + 10.
Using the formula to find x-intercept, to find the x-intercept, we just substitute y equals 0 in the given equation and solve for x.
0 = x2 - 7x + 10
0 = (x - 2) (x - 5)
x - 2 equals 0; x - 5 = 0
x equals 2; x equals 5
Answer: The x-intercepts of the given function are as follows (2, 0) and (5, 0)
Question 2) Use the formula to find the x-intercept of the rational function y = (3x - 1) / (2x + 1).
Solution:
To find: The x-intercept of the given function y = (3x - 1) / (2x + 1).
Using the x-intercept formula, we substitute y equals 0 in the above equation and solve for x.
0 equals (3x - 1) / (2x + 1)
Multiplying both sides by (2x + 1),
0 = 3x - 1
x = 1 / 3
Answer: The x-intercept of the given rational function is (1 / 3, 0)
FAQs on X-Intercept Formula
Q.1. What is X Intercept and Y Intercept?
Answer. Any straight line's equation, known as a linear equation, can be written as y = mx + b, where m is the slope of the line and b is the y-intercept. This line's y-intercept is the value of y at the point where the line intersects the y axis.
The x-intercepts are points on a function or equation's graph that cross or "touch" the x-axis of the Cartesian Plane. Consider this a point with a y-value of zero. To find an equation's x-intercepts, first let y = 0 y = 0 y equals 0 and then solve for x. It is written in point notation as (x,0).
Q.2. What is the Intercept Regression Formula?
Answer. The intercept (also known as the constant) is the expected mean value of Y when all X is equal to zero. Begin with a regression equation that has only one predictor, X. If X occasionally equals zero, the intercept is simply the expected mean value of Y at that point. If X is never equal to zero, the intercept has no inherent meaning.
The slope of a line indicates its steepness, and the intercept indicates where it intersects an axis. The slope and intercept of a linear relationship between two variables can be used to calculate the average rate of change.
