To write the equation of a line in slope-intercept form, you need to follow these steps:
1. Identify the slope (m): The slope of the line is given as [tex]\( m = 4 \)[/tex].
2. Identify a point on the line: The line passes through the point [tex]\((3, -6)\)[/tex].
3. Use the point-slope form to find the y-intercept (b):
The point-slope form of a line is [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.
Substitute the given point [tex]\((3, -6)\)[/tex] and the slope [tex]\( m = 4 \)[/tex] into the point-slope form equation:
[tex]\[
y - (-6) = 4(x - 3)
\][/tex]
Simplify the equation to solve for [tex]\( y \)[/tex]:
[tex]\[
y + 6 = 4x - 12
\][/tex]
Next, isolate [tex]\( y \)[/tex] on one side to convert the equation into slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[
y = 4x - 12 - 6
\][/tex]
Combine like terms:
[tex]\[
y = 4x - 18
\][/tex]
4. Write the final equation: The equation of the line in slope-intercept form is:
[tex]\[
y = 4x - 18
\][/tex]
Thus, the equation of the line passing through the point [tex]\((3, -6)\)[/tex] with a slope of 4 is:
[tex]\[
y = 4x - 18
\][/tex]
