Question

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Answer 1

Answer:

An equation of the line that passes through the point(2,−5) and is parallel to the line 6x+y=6 is:

• $y=-6x+7$

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where m is the slope and b is the y-intercept

Given the equation

$6x+y=6$

Writing in the slope-intercept form of the line equation

$y = -6x + 6$

comparing with the slope-intercept form of the line equation

y = mx+b

Thus, the slope of line = m = -6

We know that the parallel lines have the same slopes.

Thus, the slope of the parallel line is also -6.

As the line passes through the point (2,−5).

Thus, using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope and (x₁, x₂) is the point

substituting the values m = -6 and the point (2,−5)

$y-y_1=m\left(x-x_1\right)$

$y - (-5) = -6 (x - 2)$

$y+5=-6\left(x-2\right)$

subtract 5 from both sides

$y+5-5=-6\left(x-2\right)-5$

$y=-6x+7$

Therefore, an equation of the line that passes through the point(2,−5) and is parallel to the line 6x+y=6 is:

• $y=-6x+7$