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What is the equation of the line that passes through the point [tex]$(2,-4)$[/tex] and has a slope of [tex]-4[/tex]?

[tex]\square[/tex]

Sagot :

GinnyAnswer
Let's find the equation of the line that passes through the point [tex]\((2, -4)\)[/tex] and has a slope of [tex]\(-4\)[/tex].

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

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

where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope. Given [tex]\((x_1, y_1) = (2, -4)\)[/tex] and [tex]\(m = -4\)[/tex], we can substitute these values into the point-slope form:

[tex]\[ y - (-4) = -4(x - 2) \][/tex]

Simplify the left side of the equation:

[tex]\[ y + 4 = -4(x - 2) \][/tex]

Next, we expand the right side:

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

To get the equation into slope-intercept form [tex]\(y = mx + b\)[/tex], we need to isolate [tex]\(y\)[/tex]. Subtract 4 from both sides to achieve this:

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

Simplify the expression on the right side:

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

Therefore, the equation of the line that passes through the point [tex]\((2, -4)\)[/tex] and has a slope of [tex]\(-4\)[/tex] is:

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