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Write an equation of a line in slope intercept form that has a slope of 2/3 and goes through (9,-5).

User Jakub K
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Final answer:

The equation of the line in slope-intercept form with a slope of 2/3 that passes through the point (9,-5) is y = (2/3)x - 11.

Step-by-step explanation:

To write an equation of a line in slope-intercept form that has a slope of 2/3 and goes through the point (9,-5), we can start with the formula for a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we plug in the slope (2/3) into the equation, which gives us y = (2/3)x + b. Next, we need to find the value of b. We can do this by using the coordinates of the point the line goes through, (9,-5). Substituting these values into our equation gives us -5 = (2/3)(9) + b. We solve for b by performing the multiplication and subtracting the result from -5:

  • -5 = (2/3)×9 + b
  • -5 = 6 + b
  • -5 - 6 = b
  • b = -11

Now that we have the y-intercept, we can write the final equation of our line: y = (2/3)x - 11.

This is the big final answer for the equation of the line with a slope of 2/3 and that passes through the point (9,-5).

User Morty Choi
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