Math

QuestionFind the line equation with slope -3 passing through the point (1,2)(1,-2).

Studdy Solution

STEP 1

Assumptions1. The slope of the line is -3. The line passes through the point (1, -)

STEP 2

The equation of a line in slope-intercept form is given byy=mx+by = mx + bwhere mm is the slope of the line and bb is the y-intercept.

STEP 3

We know the slope mm is -3, so we can substitute this into the equationy=3x+by = -3x + b

STEP 4

We know the line passes through the point (1, -2). This means when x=1x =1, y=2y = -2. We can substitute these values into the equation to solve for bb2=3(1)+b-2 = -3(1) + b

STEP 5

olving the equation for bb gives2=3+b-2 = -3 + bb=2+3b = -2 +3

STEP 6

Calculate the value of bbb=2+3=1b = -2 +3 =1

STEP 7

Now we can substitute b=1b =1 back into the equation of the line to get the final equationy=3x+1y = -3x +1So, the equation of the line that has a slope of -3 and goes through the point (1,2)(1,-2) is y=3x+1y = -3x +1.

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