Question

How do you find the line with a slope of $ \dfrac{3}{4} $ that passes through $ (0,4) $ ?

Answer 1

Hint: In any linear equation, m is the slope and b is the y-intercept and this equation is known as the slope-intercept equation. Here will find the y intercept value for the standard equation and will also take one example to understand it in the better ways.

Complete step-by-step answer:
The slope of the line, “m” can be expressed as
 $ m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} $ …. (A)
Where $ ({x_1},{y_1}) = (0,4) $ and $ ({x_2},{y_2}) = (x,y) $ are the coordinates of any two points in the given line.
and $ m = \dfrac{3}{4} $
Place all the values in the equation (A)-
 $ \dfrac{3}{4} = \dfrac{{y - 4}}{{x - 0}} $
Simplify the above expression-
 $ \Rightarrow \dfrac{3}{4} = \dfrac{{y - 4}}{x} $
Do Cross multiplication where numerator of one side is multiplied to the denominator of the other side.
 $ \Rightarrow 3x = 4(y - 4) $
Multiply the constant outside the bracket.
 $ \Rightarrow 3x = 4y - 16 $
Move all the terms on the left hand side of the equation from the right hand side of the equation. When any term is moved from one side to another, the sign of the term also changes. Positive terms become negative and vice-versa.
 $ \Rightarrow 3x - 4y + 16 = 0 $
So, the correct answer is “3x - 4y + 16 = 0”.

Note: Always remember the standard form of the linear equation, slope and intercept equation as the y intercept depends on the standard equation. Always remember When any term is moved from one side to another, the sign of the term also changes. Positive terms become negative and vice-versa.
The property of the slopes of the two perpendicular lines is always equal to $ ( - 1) $ whereas slopes of two parallel lines are always equal to each other.