y = mx + c
y = mx + c refers to an equation of a line having a gradient of m and a y-intercept of c. This equation is often referred to as the slope-intercept form of the equation of a line. This equation also forms an important equation in the new science of artificial intelligence, to help predict the values, based on the input variable values.
Let us learn more about y = mx + c, its graph, and the derivation from other forms of equations of a line.
| 1. | What Is y = mx = c? |
| 2. | Graph of y = mx + c |
| 3. | Derivation of y = mx + c |
| 4. | Examples on y = mx + c |
| 5. | Practice Questions |
| 6. | FAQs on y = mx + c |
What Is y = mx + c?
The equation y = mx + c is called the slope-intercept form of the equation of the line. It requires the slope value 'm' and the y-intercept c of the line. Understanding this equation of the line requires us to first understand the slope m of the line and the y-intercept of this line.
Slope: The alphabet m represents the slope or gradient of the line. This can be a positive slope, negative slope, or zero slope. The slope can also be calculated by the tangent of the angle of inclination of this line, with reference to the x-axis.
Intercept: In this equation, the value 'c' is called the intercept of the line. The intercept measures the length where the line cuts the y-axis, from the origin. It can also be interpreted as the point (0, c) on the y-axis, through which the line is passing.
Graph of y = mx + c
The following graph shows the equation of the line y = mx + c, where m is the slope of the line, and c is the y-intercept of the line. This line cuts the y-axis at the point (0, c) which is at a distance of c units from the origin. The inclination of this line with reference to the x-axis or a line parallel to the x-axis is known by its slope m value.
The above graph has been shown with the positive values of m and c, and in the first quadrant. Further, this graph can also be presented for this equation of the line in other quadrants also.
Derivation of y = mx + c
The equation y = mx + c can be derived from other important forms of equations of a line. Some of the different forms of equations of a line from which this equation y = mx + c can be derived is as follows.
Slope Formula
The equation y = mx + c can be derived from the slope formula. Here we take a point (0, c) on the y-axis, and an arbitrary point (x, y) on the line. With these two points, we aim at finding the slope 'm' of the line. The slope of the line is the difference of the y coordinates of the two points, divided by the difference of the x coordinates of the two points.
m = (y - c)/(x - 0)
m = (y - c)/x
mx = y - c
mx + c = y
y = mx + c
Thus we are able to successfully derive the slope-intercept form of the equation of a line, using the formula for the slope of a line.
Point Slope Form
The point-slope form of the equation of a line requires a point and the slope of the line. Let us take the slope of the line as 'm' and the point as (0, c). With the help of these two values, we can find the following equations of the point-slope form of the equation of a line.
(y - c) = m(x - 0)
y - c = mx
y = mx + c
Thus we are able to successfully derive the equation y = mx + c, using the point-slope form of the equation of a line.
Related Topics
The following related topics are helpful for a better understanding of the equation y = mx + c.
FAQs on y = mx + c
What Is y = mx + c?
The expression y = mx + c is an equation of a line having the slope 'm', and the y-intercept of 'c'. This equation of a line is formed by knowing the slope of the line and the intercept which the line cuts on the y-axis. This equation y = mx + c is the basic equation of the line and can be used to form the other equations of the line.
How Do You Find the Gradient Using the Equation of the Line y = mx + c?
In the equation y = mx + c, the coefficient of x represents the gradient of the line. This gradient of the line is the 'm' value, in the equation y = mx + c. The value of m can be calculated from the angle which this line makes with the x-axis or a line parallel to the x-axis.
What is 'c' In The Equation of the Line y = mx + c?
The value of c in the equation y = mx + c represents the y-intercept of the line. The intercept is the distance from the origin on the y-axis, where this line cuts the y-axis. The value of 'c' can be easily identified after transforming any equation in the form y = mx + c, and the constant terms represent the value of 'c'.
How Do You Derive the Equation of a Line y = mx + c From Point-Slope Form?
The equation y = mx + c can be easily formed from the point-slope form of the equation of a line. Here let us assume the slope of the line as m, and the point through which the line is passing is (0, c). Applying this in the point-slope form of the equation of the line, we have the following expression.
- y - c = m(x - 0)
- y - c = mx
- y = mx + c
Here we have successfully derived the equation of the line as y = mx + c.
What Are the Other Forms of Equations of a Line, Similar to the Equation y = mx + c?
The other forms of equations of a line, apart from y = mx + c, are as follows.
- Point Slope Form: \(y - y_1 = m(x - x_1)\).
- Two Point Form: \(y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)\)
- Intercept Form: x/a + y/b = 1
- Normal Form: xCosθ + ySinθ = P