{"id":2423,"date":"2021-07-08T16:28:57","date_gmt":"2021-07-08T16:28:57","guid":{"rendered":"https:\/\/mathemerize.com\/?p=2423"},"modified":"2021-11-30T16:51:19","modified_gmt":"2021-11-30T11:21:19","slug":"find-slope-of-line","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-slope-of-line\/","title":{"rendered":"How to Calculate Slope of Line – Slope of Parallel Lines"},"content":{"rendered":"
If given line makes an angle \\(\\theta\\) (0 \\(\\le\\) \\(\\theta\\) \\(\\le\\) 180 , \\(\\theta\\) \\(\\ne\\) 90) with positive direction of x-axis, then slope of line will be tan\\(\\theta\\) and is usually denoted by letter m.<\/p>\n
\ni.e. m = tan\\(\\theta\\).<\/p>\n<\/blockquote>\n
Slope of line Passing Through Two Points Formula<\/strong><\/p>\n
If A(\\(x_1,y_1\\)) and B(\\(x_2,y_2\\)) are the two points on a straight line & \\(x_1\\) \\(\\ne\\) \\(x_2\\) then the formula for slope of line passing through two points is<\/p>\n
\nm = \\(y_2-y_1\\over {x_2-x_1}\\).<\/p>\n<\/blockquote>\n
By using above formula, we can easily calculate the slope of line between two points.<\/p>\n\n\n
Example : <\/span> Find the slope of a line between the points A = (2, 0) and B = (4,6).<\/p>\n\n
Solution : <\/span>Here \\(x_1, y_1\\) = (2, 0) and \\(x_2, y_2\\) = (4, 6).
\nBy using slope of line formula,
\nm = \\(y_2-y_1\\over {x_2-x_1}\\) = \\(6-0\\over 4-2\\)
\nm = \\(6\\over 2\\)
\n\\(\\implies\\) m = 3.
\nHence slope of line is 3.<\/p>\n\n\nSlope of Vertical Lines – Slope of Line Parallel to y-axis :<\/h2>\n
A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane.<\/p>\n
\nIn this case, \\(\\theta\\) = 90<\/p>\n
m = tan\\(\\theta\\) = tan 90 = \\(\\infty\\)<\/p>\n
i.e. m does not exist when the slope of line is parallel to y-axis.<\/p>\n<\/blockquote>\n
Slope of Horizontal Lines – Slope of Line Parallel to x-axis :<\/h2>\n
A horizontal line which is parallel to x-axis and goes straight, left and right in the coordinate plane.<\/p>\n
\nIn this case, \\(\\theta\\) = 0<\/p>\n
m = tan\\(\\theta\\) = tan 0 = 0<\/p>\n
i.e. m = 0<\/p>\n<\/blockquote>\n
Slope of Parallel Lines :<\/h2>\n
Let \\(m_1\\) and \\(m_2\\) be slopes of two given lines,<\/p>\n
\nthen, \\(m_1\\) = \\(m_2\\)<\/p>\n<\/blockquote>\n
Slope of Perpendicular Lines :<\/h2>\n
Let \\(m_1\\) and \\(m_2\\) be slopes of two given lines,<\/p>\n
\nthen, \\(m_1\\) \\(\\times\\) \\(m_2\\) = -1<\/p>\n<\/blockquote>\n
Slope of Line Equation :<\/h2>\n
The slope of line equation is also called equation of line in slope form and is written as<\/p>\n
\ny = mx + c.<\/p>\n
where m is the slope of line and c is the intercept on y-axis.<\/p>\n<\/blockquote>\n\n\n
Example : <\/span> Find the slope of a line whose equation is y = 3x + 4.<\/p>\n\n
Solution : <\/span>Given equation is y = 3x + 4
\nComparing it with slope of line equation, y = mx + c
\nwe get, m = 3.<\/p>\n\n\nHope you learnt how to calculate slope of line, learn more concepts of straight lines and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n