Question

Write an equation of the line in slope-intercept form that passes through the two points, or passes through the point and has the given slope. $$(6,5),(2,1)$$

Short answer

The equation of the line passing through the points (6,5) and (2,1) in slope-intercept form is \(y = -x + 3\)

Step-by-step solution

Determine the slope

The slope, m, of a line passing through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m = \frac{y_2 - y_1}{x_2 - x_1}\) . Plugging in the two given points gives \(m = \frac{1 - 5}{2 - 6} = -1 \)

Use point-slope form

Use the calculated slope and one of the given points, say (2,1), to write the equation in point-slope form, \(y - y_1 = m(x - x_1)\), so the equation becomes \(y - 1 = -1(x - 2)\)

Convert to slope-intercept form

To get the equation in slope-intercept form (y = mx + c), distribute the -1 on the right-hand side and add 1 to both sides, which gives \(y = -x + 3\)