To find the equation of the line that passes through the point (2, 3) and has a slope of -4, we can use the point-slope form of the equation of a line. The point-slope form 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 (2, 3)
- [tex]\( m \)[/tex] is the slope of the line (-4)
Let's go through this step-by-step:
1. Identify the given values:
- Point [tex]\((x_1, y_1) = (2, 3)\)[/tex]
- Slope [tex]\( m = -4 \)[/tex]
2. Substitute the values into the point-slope form:
[tex]\[
y - 3 = -4(x - 2)
\][/tex]
3. Simplify the equation:
- Distribute the slope [tex]\(-4\)[/tex] on the right-hand side:
[tex]\[
y - 3 = -4x + 8
\][/tex]
- To isolate [tex]\( y \)[/tex], add 3 to both sides of the equation:
[tex]\[
y = -4x + 8 + 3
\][/tex]
[tex]\[
y = -4x + 11
\][/tex]
So, the equation of the line in slope-intercept form [tex]\(y = mx + b\)[/tex] is:
[tex]\[ \boxed{y = -4x + 11} \][/tex]
This equation represents the line that passes through the point (2, 3) with a slope of -4.
