Questions: Write an equation in point-slope form of the line that passes through the given point and has the given slope. (7,-4) ; m=-2

Transcript text: Write an equation in point-slope form of the line that passes through the given point and has the given slope. \[ (7,-4) ; m=-2 \]

Solution

Solution Steps

To write the equation of a line in point-slope form, we use the formula: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the given point and \(m\) is the given slope. Plug in the values \((7, -4)\) and \(m = -2\) into the formula.

Step 1: Identify the Given Values

We are given the point \((7, -4)\) and the slope \(m = -2\).

Step 2: Apply the Point-Slope Formula

Using the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] we substitute the values: \[ y - (-4) = -2(x - 7) \]

Step 3: Simplify the Equation

This simplifies to: \[ y + 4 = -2(x - 7) \] Distributing the slope: \[ y + 4 = -2x + 14 \] Now, isolating \(y\): \[ y = -2x + 14 - 4 \] Thus, we have: \[ y = -2x + 10 \]