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What is the Slope Intercept Form of a Line?
The graph of the linear equation y = mx + c is a line with m as the slope, and m, and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
The slope, m, represents the steepness of a line. The slope of the line is also termed a gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
Here, the distance c is called the y-intercept of the given line L.
So, the coordinate of a point where the line L meets the y-axis will be
(0, c). That means line L passes through a fixed point (0, c) with slope m.
We know that, the equation of a line in point-slope form, where (x1, y1) is the point and slope m is:
(y – y1) = m(x – x1)
Here, (x1, y1) = (0, c)
Substituting these values, we get;
y – c = m(x – 0)
y – c = mx
y = mx + c
Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
Note: The value of c can be positive or negative based on the intercept made on the positive or negative side of the y-axis, respectively
Slope Intercept Form x Intercept
We can write the formula for the slope-intercept form of the equation of line L whose slope is m and x-intercept d as:
y = m(x – d)
Here,
m = Slope of the line
d = x-intercept of the line
Sometimes, the slope of a line may be expressed in terms of tangent angle such as:
m = tan θ