Question

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. $$ (5,-1), m=-1 $$

Short answer

The equation of the line in point-slope form is \(y + 1 = -x + 5\) and in slope-intercept form, it is \(y = -x + 4\).

Step-by-step solution

Write The Equation in Point-Slope Form

The point-slope form of a line is given by \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is the point through which the line passes. So, by substituting point \((5,-1)\) and slope \(-1\) to this equation we get \(y - (-1) = -1 (x - 5)\), which simplifies to \(y + 1 = -x + 5\).

Convert The Equation to Slope-Intercept Form

The slope-intercept form of a line is \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept. So, by rearranging the equation from step 1, we get \(y = -x + 5 - 1\) which further simplifies to \(y = -x + 4\).