Question

Write an equation of the line that passes through the points. (3,7),(7,3)

Short answer

The equation of the line passing through the points (3,7) and (7,3) is \(y = -x + 10\).

Step-by-step solution

Find the slope

First, find the slope using the formula \(m = \frac{{y2 - y1}}{{x2 - x1}}\), where (x1, y1) and (x2, y2) are the given points. Here, (x1, y1) = (3,7) and (x2, y2) = (7,3), so \(m = \frac{{3 - 7}}{{7 - 3}} = -1\).

Finding the y-intercept

To find the y-intercept, use the equation of a line in slope-intercept form, which is y = mx + b. Substitute any point\'s coordinates (x, y) and the slope m to find b. In this case, using point (3, 7) and m = -1, we obtain \(b = 7 - (-1) * 3 = 7 + 3 = 10\).

Writing the Final Equation

Substitute the values of m and b into the equation y = mx + b. The final line's equation that passes through the points (3,7) and (7,3) would then be written as y = -1x + 10, which simplifies to y = -x + 10.