Question

Write an equation of the line that passes through the points. (5,2),(4,3)

Short answer

The equation of the line that passes through the points (5,2) and (4,3) is \(y = -x + 7\).

Step-by-step solution

Calculate the slope

The slope of a line passing through points \((x1, y1)\) and \((x2, y2)\) can be calculated using the formula \[m = \frac{{y2 - y1}}{{x2 - x1}}\]. Substitute the given points into the formula: \(m = \frac{{3 - 2}}{{4 - 5}} = -1\).

Write the equation in point-slope form

The point-slope form of the equation of a line is \(y - y1 = m(x - x1)\). Substitute one of the given points and the calculated slope into the formula. For example, using the point (5,2) leads to: \(y - 2 = -1(x - 5)\).

Transform to slope-intercept form

Simplify the equation to the slope-intercept form \(y = mx + b\). Distribute the slope (-1) in the equation: \(y - 2 = -x + 5\). Then solve for y to get: \(y = -x + 7\).