Me i am on a test

which equation in slope-intercept form represents a line that is parallel to y=12x−2 and passes through the point (−8,1)?
y=12x−9
y=−2x−5
y=12x+5
y=−12x+5
y=−2x−7

The equation in slope-intercept form represents a line that is parallel to y = 12x − 2 and passes through the point (−8,1) is y = 12x + 97

Solution:

Given that we have to write the equation in slope intercept form for line that is parallel to y = 12x − 2 and passes through the point (−8, 1)

The slope intercept form is given as:

y = mx + c   eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given equation of line is y = 12x - 2

On comparing the above equation with eqn 1,

m = 12

Thus slope of line is 12

We know that slopes of parallel lines are equal

Therefore, slope of line parallel to given line is also 12

Given point is (-8, 1)

We have to find the equation of line passing through (-8, 1) with slope m = 12

Substitute m = 12 and (x, y) = (-8, 1) in eqn 1

1 = 12(-8) + c

1 = -96 + c

c = 97

Substitute c = 97 and m = 12 in eqn 1

y = 12x + 97

Thus the required equation of line is found

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