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Write the equation of a line that has a slope of -4 and passes through the point (6, 8).

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GinnyAnswer
Certainly! Let's write the equation of a line that has a slope of [tex]\( -4 \)[/tex] and passes through the point [tex]\((6,8)\)[/tex].

To find the equation of the line, we can use the point-slope form of the equation of a line, which is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\( m \)[/tex] is the slope of the line and [tex]\((x_1, y_1)\)[/tex] is a point on the line.

Here, the slope ([tex]\( m \)[/tex]) is [tex]\( -4 \)[/tex] and the given point [tex]\((x_1, y_1)\)[/tex] is [tex]\((6,8)\)[/tex]. Plugging these values into the point-slope form, we get:

[tex]\[ y - 8 = -4(x - 6) \][/tex]

Next, we'll distribute the slope [tex]\( -4 \)[/tex] on the right-hand side:

[tex]\[ y - 8 = -4x + 24 \][/tex]

To convert this into the slope-intercept form ([tex]\( y = mx + b \)[/tex]), we need to isolate [tex]\( y \)[/tex]:

[tex]\[ y = -4x + 24 + 8 \][/tex]

[tex]\[ y = -4x + 32 \][/tex]

Therefore, the equation of the line that has a slope of [tex]\( -4 \)[/tex] and passes through the point [tex]\((6,8)\)[/tex] is:

[tex]\[ y = -4x + 32 \][/tex]
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