Question

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(7,3), m=-2$$

Short answer

The equation of the line in standard form is \(2x + y = 17\).

Step-by-step solution

Write in Point-Slope Form

The point-slope form of a line's equation is given by \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a given point the line passes through. In this case, substituting \((7,3)\) for \((x_1,y_1)\) and \(-2\) for \(m\), we get \(y - 3 = -2(x - 7)\).

Simplify the Equation

Now simplify the equation. Distribute \(-2\) to the terms inside the parenthesis to obtain \(y - 3 = -2x + 14\).

Convert to Standard Form

The standard form of a line's equation is \(Ax + By = C\). We must convert our equation into this form. By moving \(2x\) from right to left and \(3\) from left to right, we obtain \(2x + y = 17\).