Find an equation of the line that passes through the point (7, 2) and has the indicated slope -3.

We will use the concept of the point-slope form of a straight line to find the equation.

Answer: The equation in slope-intercept form of the line through the point P(7, 2) with slope -3 is given as y = -3x + 23.

Let us see how we will use the concept of the point-slope form of the straight line to find the equation.

Explanation:

We will use the definition of slope to solve this question.

Let us consider another point on the line that is (x, y).

We know that with the given two points (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)), the slope is given by,

Slope(m) = (\(y_{2}\) - \(y_{1}\)) / (\(x_{2}\) - \(x_{1}\))

Hence, the slope of the line passing through the points (7, 2) and (x, y) is,

Slope =  (y - 2) / (x - 7) = -3  [Since, slope = -3 (given)]

⇒ y - 2 = -3 (x - 7)

⇒ y = -3x + 21 + 2

⇒ y = -3x + 23

Thus, y = -3x + 23 is the equation of the required line.