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Write the equation of the line that passes through (3, 4) and (2, -1) in slope-intercept form.

User Yingch Xue
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1 Answer

4 votes

Answer:

y = 5x - 11

Explanation:

General equation for the slope-intercept form:

The general equation for the slope-intercept form 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.

Finding the slope (m):

We can find the slope (m) using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where

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

Thus, we can find the slope (m) by substituting (3, 4) for (x1, y1) and (2, -1) for (x2, y2) in the slope formula:

m = (-1 - 4) / (2 - 3)

m = (-5) / (-1)

m = 5

Thus, the slope (m) of the line is 5.

Finding the y-intercept (b):

Now we can find the y-intercept (b) of the line by plugging in 5 for m and (3, 4) for (x, y) in the slope-intercept form:

4 = 5(3) + b

(4 = 15 + b) - 15

-11 = b

Thus, the y-intercept (b) of the line is -11.

Compiling the equation in slope-intercept form:

Therefore, y = 5x - 11 is the equation of the line in slope-intercept form passing through (3, 4) and (2, -1).

User Paul Hargreaves
by
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