Question
A line passes through (9, -9) and (10, -5).Write an equation for the line in point-slope form. Rewrite the equation in standard form using integers.
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GPT 3.5
To find the equation of the line passing through the points (9, -9) and (10, -5) in point-slope form, we first need to find the slope of the line.
The slope (m) can be found using the formula:
m = (y2 - y1)/(x2 - x1)
m = (-5 - (-9))/(10 - 9)
m = (-5 + 9)/(10 - 9)
m = 4
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (9, -9):
y - (-9) = 4(x - 9)
y + 9 = 4(x - 9)
y + 9 = 4x - 36
Finally, rewriting the equation in standard form using integers:
y + 9 = 4x - 36
y = 4x - 45
Therefore, the equation of the line passing through the points (9, -9) and (10, -5) in point-slope form is y + 9 = 4(x - 9) and in standard form is y = 4x - 45.
The slope (m) can be found using the formula:
m = (y2 - y1)/(x2 - x1)
m = (-5 - (-9))/(10 - 9)
m = (-5 + 9)/(10 - 9)
m = 4
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (9, -9):
y - (-9) = 4(x - 9)
y + 9 = 4(x - 9)
y + 9 = 4x - 36
Finally, rewriting the equation in standard form using integers:
y + 9 = 4x - 36
y = 4x - 45
Therefore, the equation of the line passing through the points (9, -9) and (10, -5) in point-slope form is y + 9 = 4(x - 9) and in standard form is y = 4x - 45.
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