<h2><em>The Equation of line with points (4 , - 3) and slope 3/2 is y = 3/2 x - 9
</em></h2><h2><em>
</em></h2><h2><em>Step-by-step explanation:
</em></h2><h2><em>
</em></h2><h2><em>Given equation of line as :
</em></h2><h2><em>
</em></h2><h2><em> y =-2/3 x + 6
</em></h2><h2><em>
</em></h2><h2><em>∵ Standard equation of line is give as
</em></h2><h2><em>
</em></h2><h2><em>y = a x + c
</em></h2><h2><em>
</em></h2><h2><em>Where m is the slope of line and c is the y-intercept
</em></h2><h2><em>
</em></h2><h2><em>Now, comparing given line equation with standard eq
</em></h2><h2><em>
</em></h2><h2><em>So, The slope of the given line = a = -2/3</em></h2><h2><em>
</em></h2><h2><em>Again,
</em></h2><h2><em>
</em></h2><h2><em>The other line if passing through the points (- 2 , - 1 ) And is perpendicular to given line
</em></h2><h2><em>
</em></h2><h2><em>So, for perpendicular lines condition , the products of slope of both lines = - 1
</em></h2><h2><em>
</em></h2><h2><em>Let The slope of other line = m
</em></h2><h2><em>
</em></h2><h2><em>So, m × a = - 1
</em></h2><h2><em>
</em></h2><h2><em>Or, m × -2/3 = - 1
</em></h2><h2><em>
</em></h2><h2><em>So, m = -1/-2/3</em></h2><h2><em>
</em></h2><h2><em>∴ m = 3/2</em></h2><h2><em>
</em></h2><h2><em>Now, Again
</em></h2><h2><em>
</em></h2><h2><em>The line n is parallel to the line m and passes through the points (4 , - 3)
</em></h2><h2><em>
</em></h2><h2><em>∵ Line n parallel to line m so, The slope of both are equal
</em></h2><h2><em>
</em></h2><h2><em>Let The slope of line n is M
</em></h2><h2><em>
</em></h2><h2><em>So, M = m =
3/2</em></h2><h2><em>
</em></h2><h2><em>So, The equation of line written as
</em></h2><h2><em>
</em></h2><h2><em>y = M x + c
</em></h2><h2><em>
</em></h2><h2><em>Or, - 3 = 3/2 ( 4 ) + c
</em></h2><h2><em>
</em></h2><h2><em>Or, - 3 = 3*4/2 + c
</em></h2><h2><em>
</em></h2><h2><em>Or, - 3 = 6 + c
</em></h2><h2><em>
</em></h2><h2><em>Or, c = - 3 - 6
</em></h2><h2><em>
</em></h2><h2><em>∴ c = - 9
</em></h2><h2><em>
</em></h2><h2><em>So, Equation of line with points (4 , - 3) and slope 3/2 is
</em></h2><h2><em>
</em></h2><h2><em>y = 3/2 x - 9
</em></h2><h2><em>
</em></h2><h2><em>Hence , The Equation of line with points (4 , - 3) and slope 3/2 is y = 3/2 x - 9</em></h2><h2><em /></h2><h2><em> HOPE IT HELPS (◕‿◕✿) </em></h2><h2><em> SMILE!!</em></h2>
