write the equation of this line 3 2 and state its slopeSolut

write the equation of this line (3, -2) and state its slope

Solution

The equation of a line can be determined only if either two points through which it passes are given or a point and its slope are known.

Here, since only one point is given and it is desired to determine the slope, we presume that the other point is the origin i.e. (0, 0). Now, we know that the slope of the line passing through the points (x₁ , y₁ ) and ( x₂ , y₂ ) is (y₂ - y₁ )/( x₂ - x₁ ). Hence, the slope of the given line is [ 0 - (-2)]/( 0-3) = 2/-3 = -2/3. Now, we also know that the slope-intercept form of the equation of a line is y = mx + c where m is the slope and c is the y-intercept. Here m = -2/3 so the equation changes to y = -2x/3 + c. Further, since the line passes through the point (3,-2), on substituting x = 3 and y = -2 in this equation, we get -2 = (-2/3)*3 +c or, -2 = -2 +c so that c = 0. Then, the equation of the line is y = -2x/3.