Find an equation of the line with the given slope that passes through the given point. Write the equation in the form Ax + By = C.
m = -1, (-7, -4)
The equation of the line in the form Ax + By = C is [ ]. (Simplify your answer. Use integers or fractions for any numbers in the equation.)
To find the equation of the line, we can use the point-slope formula: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the slope m = -1 and the point (-7, -4), we have:
y - (-4) = -1(x - (-7))
y + 4 = -x - 7
Now, let's rearrange the equation to the form Ax + By = C:
x + y + 11 = 0
Therefore, the equation of the line with a slope of -1 that passes through the point (-7, -4) is x + y + 11 = 0.
that was incorrect
I apologize for the mistake. Let's correct it.
Using the point-slope formula, we have:
y - y1 = m(x - x1)
Substituting m = -1 and the point (-7, -4), we have:
y - (-4) = -1(x - (-7))
y + 4 = -1(x + 7)
y + 4 = -x - 7
Now, let's rearrange the equation to the form Ax + By = C:
x + y + 7 = 0
Therefore, the equation of the line with a slope of -1 that passes through the point (-7, -4) is x + y + 7 = 0.
that was incorrect. write it in standard form
Apologies once again for the mistake. Let's write the equation in standard form.
Starting with the equation we derived:
y + 4 = -x - 7
Rearranging the equation by bringing all the terms to one side:
x + y + 7 = 0
Therefore, the equation of the line with a slope of -1 that passes through the point (-7, -4) in standard form is x + y + 7 = 0.
To find an equation of a line passing through a given point and with a given slope, you can use the point-slope form of a linear equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point, and m is the slope.
In this case, the slope (m) is -1 and the given point is (-7, -4). Substituting these values into the point-slope form, we get:
y - (-4) = (-1)(x - (-7))
Simplifying this equation, we have:
y + 4 = -x + 7
To rewrite the equation in the form Ax + By = C, we need to rearrange it by moving the variables to one side and the constant term to the other side:
x + y + 3 = 0
So, the equation of the line, in the form Ax + By = C, is x + y + 3 = 0.