Question

How do you write the equation in standard form given \[m = 4\] and \[(4,3)\]?

Answer 1

Hint: Use point-slope formula to write the equation of the line passing through the given point and having the slope of the given equation of line.
* Point-slope formula: Equation of line passing through the point \[({x_1},{y_1})\] and having slope ‘m’ is given by \[y - {y_1} = m(x - {x_1})\].

Complete step-by-step answer:
We are given a line having slope \[m = 4\] and that the line passes through the point \[(4,3)\]
We know that the equation of line having slope m and passing through the point \[({x_1},{y_1})\] can be written using the point slope formula i.e. \[y - {y_1} = m(x - {x_1})\]
Comparing the values given in the question we get \[m = 4\]and point \[({x_1},{y_1}) = (4,3)\]
Substitute the value of \[m = 4\] and \[{x_1} = 4;{y_1} = 3\] in the point slope formula
\[ \Rightarrow y - 3 = 4 \times (x - 4)\]
\[\therefore \] The point slope form of the line passing through point \[(4,3)\] and having slope \[4\] is \[y - 3 = 4(x - 4)\]

Note:
Many students make the mistake of solving the complete equation and write the final answer by bringing all terms to the left side of the equation which is not required here. We have to give the answer in point-slope form to which we can see and tell the value of the point and the slope.
The standard form of the equation is given as \[y - 3 = 4(x - 4)\]
We can further solve the equation to bring it general form i.e. \[y = mx + c\]
\[ \Rightarrow y - 3 = 4 \times (x - 4)\]
Multiply the terms outside the bracket to the terms inside the brackets on right hand side of the equation
\[ \Rightarrow y - 3 = 4 \times x - 4 \times 4\]
Calculate the products on both sides of the equation
\[ \Rightarrow y - 3 = 4x - 16\]
Bring all constant values to right hand side of the equation
\[ \Rightarrow y = 4x - 16 + 3\]
\[ \Rightarrow y = 4x - 13\]
So, the general equation of line passing through the point \[(4,3)\] and having slope 4 is \[y = 4x - 13\].