Lesson Equation for a straight line having a given slope and passing through a given point

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Equation for a straight line having a given slope and passing through a given point

An equation of a straight line in a coordinate plane which has the slope m and passes through the given point P = (a,b) is

y - b = m*(x-a). (1)

Problem 1

Find an equation of a straight line which has the slope 2 and passes through the point (4,5).

Solution

Simply substitute the given data into equation  (1),  and you will get

    y-5 = 2*(x-4).             (2)


It is the equation in the  "slope intercept form".


If you want to get the standard form equation,  simplify  (2):

   y-5 = 2x - 8,    or,  equivalently,    2x - y = 8 - 5,

or,  finally,   2x-y = 3.

Problem 2

Find an equation of a straight line which has the slope -3 and passes through the point (-2,-4).

Solution

Simply substitute the given data into equation  (1),  and you will get

    y-(-4) = (-3)*(x-(-2)).             (3)


It is the equation in the  "slope intercept form".


If you want to get the standard form equation,  simplify  (2):

   y+4 = -3x - 6,   or,  equivalently,    3x - y = -6 - 4,

or,  finally,   3x+y = -10.

My other lessons in this site related to the slope of a straight line are
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point
    - Finding a point in a segment [AB] between endpoints A and B in a coordinate plane
    - Miscellaneous problems on equations of straight lines in a coordinate plane
    - Advanced problems on finding equations for straight lines
    - Math Circle level problem on finding equation of a line
    - A tricky problem on a parabola and a straight normal line
    - Equations of straight lines in 3D space
    - OVERVIEW of lessons related to the slope of a straight line

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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