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.
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.
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