How do you write an equation of a line with slope of -3 and passing through (-2,4)?

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Mar 9, 2018

Answer:

#y = -3x - 2#

Explanation:

There are three ways to write the equation of a line: slope intercept form, point slope form, and standard (general) form.

Slope Intercept Form:

#y = mx + b#
where m is the slope of the line #((Delta y) / (Delta x))# and b is the y-intercept.
For a line with slope -3 and point (-2,4), plug -3 in for m, -2 for x, 4 for y, and solve for b.
#4 = (-3)*(-2) +b#
#4 = 6 + b#
#-2 = b#
The equation in slope intercept form is #y = -3x - 2#

Point Slope Form:

#(y-y_1) = m(x-x_1)#
Where m is the slope of the line #((Delta y) / (Delta x))#, #y_1# is the y coordinate of a point, and #x_1# is the x coordinate of a point.

For a line with slope -3 and point (-2,4), plug -3 in for m, -2 for #x_1#, 4 for #y_1#.
#(y - 4) = -3(x + 2)#

Standard Form:

Ax + By = C

Where A, B, and C are integers. To write an equation in standard form, rewrite the equation in point slope form so that it fits the formula for standard form.
#(y - 4) = -3(x + 2)#
#y - 4 = -3x - 6#
#y + 3x - 4 = - 6#

#y + 3x = - 2#

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Write your answer here...
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Answer

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Answer:

Explanation

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1
Mar 9, 2018

Answer:

#y=-3x-2#

Explanation:

Given -

Slope of the line #-3#

Point #(-2, 4)#

Use the formula -

#mx+c=y#

Where -

#m# slope of the line
#x, y# x and y coordinates, through which the line passes

in our case -

#m=-3#
#x=-2#
#y=4#

#(-3)(-2) +C=4#

#6+c=4#

#c=4-6=-2#

#-3x-2=y#

The equation of the required line is

#y=-3x-2#

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