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Find the slope and intercept of \[3x + y = - 4\] .

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Last updated date: 15th Jul 2024
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Answer
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Hint: The equation of the line is typically written as \[y = mx + b\] where “m” is the slope and “b” is the y-intercept that is the value where the line cuts the y-axis. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables.

Complete step-by-step answer:
We begin by writing in the form of \[y = mx + b\] from the equation given \[3x + y = - 4\] ,
The advantage to having the equation in this form is that “m” and “b” may be extracted easily.
Hence expressing \[3x + y = - 4\] in this form first we need to subtract \[3x\] from both the sides we have,
 \[
  3x + y - 3x = - 3x - 4 \\
   \Rightarrow y = - 3x - 4 \;
 \]
Now, \[y = - 3x - 4\] is in slope intercept form.
Hence now we can compare with the equation of the line that is Tthe equation of the line is typically written as \[y = mx + b\] where “m” is the slope and “b” is the y-intercept that is the value where the line cuts the y-axis we have,
Slope as \[ - 3\] and intercept as \[ - 4\] .
So, the correct answer is “Slope as \[ - 3\] and intercept as \[ - 4\] ”.

Note: If we are given the slope and one point then these values can be substituted into a formula which is based on the definition for slope that is \[y - {y_1} = m\left( {x - {x_1}} \right)\] . The values of “m” and “b” should be obtained by comparing with the line equation only. The slope of the line is the value of “m” and the “y” intercept is the value of “b”. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions.