Question

Write an equation of the line that passes through the points. (5,1),(3,-6)

Short answer

The equation of the line that passes through the points (5,1) and (3,-6) is \(y = 3.5x - 7.5\)

Step-by-step solution

Calculate the slope

To calculate the slope \(m\) of the line, use the formula \(m = (y_2 - y_1) / (x_2 - x_1)\), substituting the given points (5,1) and (3,-6) into the formula. This gives: \(m = (-6 - 1) / (3 - 5) = -7 / -2 = 3.5\).

Insert the slope and a point into the line equation

Next, substitute the slope and a point into the line equation. The slope is \(m = 3.5\) and the y-intercept \((x,y)\) can be any of the given points, so use (5,1). This gives: \(1 = 3.5 * 5 + c\).

Solve for y-intercept

Solving the above equation for \(c\), the y-intercept, gives \(c = 1 - 3.5 * 5 = -7.5\).