Question

How do you write an equation of the line with slope -3 and y-intercept \[(0, - 5)\] .

Answer 1

Hint: We first find the value of slope by comparing the given equation of line to the general equation of line. Use the concept of parallel lines having the same slope and write slope of the parallel line equal to slope of given line. Use slope intercept form to write the equation of the line having y-intercept and having the slope of the given equation of line.
$*$ General equation of the line is \[y = mx + c\] , where ‘m’ is the slope of the line and ‘c’ is the value of the y-intercept.

Complete step by step solution:
We know general equation of a line using slope intercept form is given by \[y = mx + c\]
Now use slope intercept formula with slope \[m = - 3\] and y-intercept as -5
So, equation of line with slope \[m = - 3\] and y-intercept -5 is:
\[ \Rightarrow y = - 3x + ( - 5)\]
Multiply sign outside the bracket to the sign inside the bracket
\[ \Rightarrow y = - 3x - 5\]
Take all values to left hand side of the equation
\[ \Rightarrow 3x + y + 5 = 0\]
\[\therefore \] The equation of the line having slope as -3 and having y-intercept -2 is \[3x + y + 5 = 0\].

Note: Many students make the mistake of substituting both the values from the point i.e. x as 0 and y as -5 while forming the equation of line which is wrong. Keep in mind in slope intercept form, c is the value of y-intercept i.e. observing the point given we have to see only the ordinate part of the point. If we substitute both values of ‘x’ and ‘y’ from the point given, we will get an equation only with variable ‘y’ which can be solved as y equal to some constant value which gives us slope as 0, which is a contradiction.