Write an equation of the line containing the point ( 4, 3) and parallel to the line having slope 4.
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(4, 3) and parallel to the line having slope 4 is given as y = 4x - 13.
Let us see how we will use the concept of the point-slope form of the straight line to find the equation.
We will use the definition of slope to find the slope
Let us consider another point on the line that is (x, y).
We know that given two points (x1,y1) and (x2,y2) the slope is given by,
Slope(m) = (y2 - y1) / (x2 - x1)
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