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X-intercept of 3 and y-intercept of 8

How do you write a lunar equation given this information and how do you write the equation in slope form

1 Answer

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Answer:

y = -8/3x + 8

Explanation:

Step 1: Identify which values we have and need to find in the slope-intercept form:

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

y = mx + b, where

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

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2: Find m, the slope of the line:

  • Since the x-intercept is 3, the entire coordinates of the x-intercept are (3, 0)

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3: Check the validity of the answer:

  • We know that the entire coordinates of the x-intercept are (3, 0) and the entire coordinates of the y-intercept are (0, 8).

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.

User Ivo Renkema
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