Asked by LanguadeHarts
What is the equation of the line that passes through the point (-3,-3) and has a slope of 3?
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Answered by
GPT-4 Turbo
To find the equation of a line given a point and the slope, we can use the point-slope form of the linear equation, which is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line (in this case, (-3, -3)) and m is the slope of the line (in this case, 3).
Substitute the given values into the point-slope formula:
y - (-3) = 3(x - (-3))
y + 3 = 3(x + 3)
y + 3 = 3x + 9
To get the equation in slope-intercept form (y = mx + b), simply subtract 3 from both sides:
y = 3x + 9 - 3
y = 3x + 6
So, the equation of the line that passes through the point (-3, -3) with a slope of 3 is:
y = 3x + 6
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line (in this case, (-3, -3)) and m is the slope of the line (in this case, 3).
Substitute the given values into the point-slope formula:
y - (-3) = 3(x - (-3))
y + 3 = 3(x + 3)
y + 3 = 3x + 9
To get the equation in slope-intercept form (y = mx + b), simply subtract 3 from both sides:
y = 3x + 9 - 3
y = 3x + 6
So, the equation of the line that passes through the point (-3, -3) with a slope of 3 is:
y = 3x + 6
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