Find the equation of a line with slope $$ - 1$$ and cutting off an intercept of 4 units on the negative direction of the y-axis.

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Vedantu Content Team · Accepted Answer

Hint: Here we use the slope form of a given line which is $$y = mx + c$$. Then we try to find the equation of the line using the given values of m and c.Complete step by step answer:Given, a line with slope $$ - 1$$, so, we have, slope (m) $$ =  - 1$$And it is cutting off an intercept of 4 units on the negative direction of the y-axis.So, we have, as per, the slope form of the a line,$$y = mx + c$$, here, $$c =  - 4$$,Then, we have the equation of line as, $$y = mx + c$$ and $$c =  - 4$$,$$m =  - 1$$,On substituting the values we get,$$y = ( - 1)x + ( - 4)$$$$ \Rightarrow y =  - x - 4$$$$ \Rightarrow y + x + 4 = 0$$This is our desired equation of the line.Note: The equation of a straight line in the slope form is given by  $$y = mx + c$$ where m is the slope and c is a desired constant. Here in this problem, as it is cutting off an intercept of 4 units on negative direction of y-axis, for, $$x = 0,$$we must have, $$y =  - 4$$. And that is what we are getting from our answer. So we can check that our answer is correct.

Find the equation of a line with slope \[ - 1\] and cutting off an intercept of 4 units on the negative direction of the y-axis.

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Find the equation of a line with slope \[ - 1\] and cutting off an intercept of 4 units on the negative direction of the y-axis.

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