Slope & y-intercept of a Line

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Since, we have already discussed the slope intercept form of the equation of a line; we will now learn how to find the slope & y-intercept for any given equation of line.

Recall that, the length of the intercept made by of a line on the Y-axis is called its y-intercept & using Slope Intercept form the equation of a line with slope or gradient m and making an y-intercept of c units is given by y = mx + c.

Slope & y-intercept of a Line
Slope & y-intercept of a Line

 

If the equation of the given line is a x + by + d = 0.

We rewrite the given equation in the slope intercept form by taking the term containing, x & constant, d on the other side of the equation i.e. by = – a x – d or y =\frac{-a}{b}\times – d or y = \frac{-a}{b}\times +\frac{-d}{b}

& then compare this with y = mx + c we have slope m =\frac{-a}{b} &  y intercept c=\frac{-d}{b}

Slope & y-intercept of a Line

Let us take a few examples

Example:

  1.  Find the slope & y-intercept of the line x+y=7.Here, we can rewrite the equation as y = – x + 7 = (-1)x + 7.Hence here slope m = (-1) & y-intercept, c = 7.
  2. Find the slope & y-intercept of the line 4x + 2y = 8.Here, we can rewrite the equation as 2y = – 4x + 8 = (-4)x + 8.or y = (-2)x + 4.Hence here slope m = (-2) & y-intercept, c = 4.
  3. Find the slope & y-intercept of the line 7x + 8y – 15 = 0.Here, we can rewrite the equation as 8y = –7x + 15 = (-7)x + (15). y=\frac{-7}{8} & y-intercept, c = \frac{15}{8}.Hence here slope m = \frac{-7}{8} & y-intercept, c= \frac{15}{8}.
  4. Here, we can rewrite the equation as y = (0)x + 0.Hence here slope, m = 0 & y-intercept, c = 0.Find the slope & y-intercept of the line y = 0.

CHECK POINT 

  1. Find the slope & y intercept of the line x + y – 75 = 8.
  2. Find the slope & y intercept of the line 3x – 7y + 105 =0.
  3. Find the slope & y intercept of the line 10x + 2y =26.
  4. Find the slope & y intercept of the line 15x – 3y + 75 = 0.
  5. Find the slope & y intercept of the line 24x + 8y =96.
Answer key
  1. Slope m = (-1), y-intercept = 83.
  2. Slope m = \frac{3}{7} , y-intercept =15.
  3. Slope m = (-5), y-intercept =13.
  4. Slope = 5, y-intercept =25.
  5. Slope m = (-3), y-intercept = 12.

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