Slope Coefficient
Introduction to slope coefficient :
In mathematics, the slope or gradient of a line describes its steepness, inclination or grade. A higher slope value indicates a steeper inclination.
The slope is defined as the part of the "rise" divided by the "run" between two points on a line or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is
M=(y2-y1)/(x2-x1)
Through degree of difference calculus, one can calculate the slope of the tangent line to a curve at a point.
The slope of the equation is explained with the help of the letter m, used to represent slope.
How does one find the slope of a line?
Given two points (x1, y1) and (x2, y2) on a line, the slope may be found by the formula
m= (y2-y2)/(x2-x1)
For an equation in slope-intercept form, y = mx + b, the slope is m, the coefficient of the x term
In the equation Ax + By = C, the slope is given by m = - A/B
What is the equation of the line which passes through the point (- 5, 8) with a slope of - 4 in standard form with integer coefficients?
Solution:
Step1: The equation of the line passing through the point (x1, y1) with slope m in point-slope form is y - y1 = m(x - x1).
Step 2: Point (x1, y1) = (- 5, 8) and slope m = - 4.
Step3 y - 8 = - 4[x - (-5)]
[Substitute x1 = - 5, y1 = 8 and m = -4 ]
Step 4: y - 8 = - 4x - 2 0
[Distribute -4.]
Step 5: y = - 4x + (-12)
[Add 8 to each side.]
Step6:4x + y = -12
[Add4x to each side.]
Step7: The equation of the line in standard form is 4x + y = -12.
