Answered

From simple questions to complex issues, IDNLearn.com has the answers you need. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

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 :

GinnyAnsweridn
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]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.