y = mx + c
y = mx + c refers to an equation of a line having a gradient of m and a yintercept of c. This equation is often referred to as the slopeintercept 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 slopeintercept form of the equation of the line. It requires the slope value 'm' and the yintercept c of the line. Understanding this equation of the line requires us to first understand the slope m of the line and the yintercept 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 xaxis.
Intercept: In this equation, the value 'c' is called the intercept of the line. The intercept measures the length where the line cuts the yaxis, from the origin. It can also be interpreted as the point (0, c) on the yaxis, 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 yintercept of the line. This line cuts the yaxis 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 xaxis or a line parallel to the xaxis 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 yaxis, 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 slopeintercept form of the equation of a line, using the formula for the slope of a line.
Point Slope Form
The pointslope 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 pointslope 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 pointslope 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.
Examples on y = mx + c

Example 1: Find the equation of a line in the form y = mx + c, having a slope of 3 units and an intercept of 5 units.
Solution:
Given the slope of the line, m = 3, and the yintercept of the line, c = 5.
The slopeintercept form of the equation of a line is y = mx + c.
y = 3x  5
Answer: Therefore the required equation of the line is y = 3x  5.

Example 2: Convert the equation 5x + 4y = 12 into y = mx + c and find its yintercept.
Solution:
The given equation of the line is 5x + 4y = 12. The aim is to convert this into slope intercept form.
5x + 4y = 12
4y = 5x + 12
y = (5x + 12)/4
y = 5x/4 + 12/4
y = 5x/4 + 3
Comparing this with the equation y = mx + c we have m = 5/4, and c = 3.
Answer: Therefore the yintercept of the line is 3.
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 yintercept 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 yaxis. 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 xaxis or a line parallel to the xaxis.
What is 'c' In The Equation of the Line y = mx + c?
The value of c in the equation y = mx + c represents the yintercept of the line. The intercept is the distance from the origin on the yaxis, where this line cuts the yaxis. 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 PointSlope Form?
The equation y = mx + c can be easily formed from the pointslope 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 pointslope 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
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