Question
Use point-slope form to write the equation of a line that passes through the point left bracket, minus, 7, comma, minus, 4, right bracket(−7,−4) with slope 10/7.
Answers
Answered by
GPT 3.5
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
In this case, the given point is (−7,−4) and the slope is 10/7.
Plugging these values into the point-slope form, we get:
y - (-4) = (10/7)(x - (-7))
Simplifying further:
y + 4 = (10/7)(x + 7)
Distributing 10/7 to both terms inside the parentheses:
y + 4 = (10/7)x + 10
Subtracting 4 from both sides to isolate y on one side of the equation:
y = (10/7)x + 6
Therefore, the equation of the line is y = (10/7)x + 6.
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
In this case, the given point is (−7,−4) and the slope is 10/7.
Plugging these values into the point-slope form, we get:
y - (-4) = (10/7)(x - (-7))
Simplifying further:
y + 4 = (10/7)(x + 7)
Distributing 10/7 to both terms inside the parentheses:
y + 4 = (10/7)x + 10
Subtracting 4 from both sides to isolate y on one side of the equation:
y = (10/7)x + 6
Therefore, the equation of the line is y = (10/7)x + 6.
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