Write an equation of the line containing the point (4, 3) and parallel to the line having slope 4.

Solution:

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

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,

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

Hence, the slope of the line passing through the points (4, 3) and (x, y) is,

Slope =  (y - 3) / (x - 4) = 4  [Since, slope = 4 (given)]

⇒ y - 3 = 4 (x - 4)

⇒ y = 4x - 16 + 3

⇒ y = 4x - 13

Thus, y = 4x - 13 is the equation of the required line.

Write an equation of the line containing the point (4, 3) and parallel to the line having slope 4.

Summary:

The equation in slope-intercept form of the line through the point P(4, 3) and parallel to the line having slope 4 is given as y = 4x - 13.