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).