Answer :
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]
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]
