A line passes through the point (-10,6) and has a slope of -(3)/(2) Write an equation in point-slope form for this line. square

To write the equation of a line in point-slope form, we use the formula:<br /><br />\[ y - y_1 = m(x - x_1) \]<br /><br />where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.<br /><br />Given:<br />- Point: \((-10, 6)\)<br />- Slope: \(m = -\frac{3}{2}\)<br /><br />Substitute the given point and slope into the point-slope formula:<br /><br />\[ y - 6 = -\frac{3}{2}(x - (-10)) \]<br /><br />Simplify the expression inside the parentheses:<br /><br />\[ y - 6 =}{2}(x + 10) \]<br /><br />So, the equation in point-slope form for the line passing through the point \((-10, 6)\) with a slope of \(-\frac{3}{2}\) is:<br /><br />\[ y - 6 = -\frac{3}{2}(x + 10) \]