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Write equations of a line in slope intercept form going through the points 2,1 and -1,-5

User Wahaj Ali
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Answer:

Equation of the line in slope-intercept form: y = 2x - 3

Explanation:

The general equation of the sloe-intercept form of a line is given by:

y = mx + b, where

  • (x, y) is any point on the line,
  • m is the slope,
  • and b is the y-intercept.

Step 1: Find m, the slope:

We can find m, the slope of the line using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where:

  • m is the slope,
  • (x1, y1) is one point,
  • and (x2, y2) is another point.

Thus, we can plug in (2, 1) for (x1, y1) and (-1, -5) for (x2, y2) to find m, the slope of the line:

m = (-5 - 1) / (-1 - 2)

m = (-6) / (-3)

m = 2

Thus, the slope of the line is 2.

Step 2: Find b, the y-intercept of the line:

We can find b, the y-intercept of the line by plugging in any of the two points for (x, y) and 2 for m in the slope-intercept form. Let's use (2, 1) for (x, y):

1 = 2(2) + b

1 = 4 + b

-3 = b

Thus, the y-intercept of the line is -3.

Therefore, the equation of a line in slope-intercept form passing through the points (2, 1) and (-1, -5) is y = 2x - 3

User Auzy
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