Questions: Find an equation of the line with the slope m=-6 that passes through the point (-2,-4). Write the equation in the form A x+B y=C. Choose the correct answer below. A. 6 x+y=-16 B. 6 x+y=16 C. 16 x+y=6 D. 16 x+y=-6

Find an equation of the line with the slope m=-6 that passes through the point (-2,-4). Write the equation in the form A x+B y=C.

Choose the correct answer below.
A. 6 x+y=-16
B. 6 x+y=16
C. 16 x+y=6
D. 16 x+y=-6

Transcript text: Find an equation of the line with the slope $m=-6$ that passes through the point $(-2,-4)$. Write the equation in the form $A x+B y=C$. Choose the correct answer below. A. $6 x+y=-16$ B. $6 x+y=16$ C. $16 x+y=6$ D. $16 x+y=-6$

Solution

Solution Steps

Step 1: Start with the point-slope form of the line equation

Given the slope $m = -6$ and a point $(-2, -4)$, the point-slope form is $y + 4 = -6(x + 2)$.

Step 2: Convert to the slope-intercept form $y = mx + b$

Rearranging the point-slope form, we find the y-intercept $b = -4 + 6*-2 = -16$. So, the slope-intercept form is $y = -6x - 16$.

Step 3: Convert to the standard form $Ax + By = C$

Rearranging terms, we get $-6x - y = -16$, which simplifies to $6x + (1)y = 16$.

Final Answer:

The equation of the line in standard form is $6x + (1)y = 16$.

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