Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

Sagot :

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]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.