To find the equation of a line in slope-intercept form [tex]\( y = mx + b \)[/tex], we need to determine the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex]. We are given the slope [tex]\( m = 3 \)[/tex] and a point on the line [tex]\((-2, 2)\)[/tex].
Here's the step-by-step process:
1. Substitute the slope and the point into the point-slope form of the equation:
The point-slope form is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Given:
- Slope [tex]\( m = 3 \)[/tex]
- Point [tex]\((x_1, y_1) = (-2, 2)\)[/tex]
Substitute these values in:
[tex]\[
y - 2 = 3(x - (-2))
\][/tex]
Simplify inside the parenthesis:
[tex]\[
y - 2 = 3(x + 2)
\][/tex]
2. Distribute the slope (3) on the right-hand side:
[tex]\[
y - 2 = 3x + 6
\][/tex]
3. Solve for [tex]\( y \)[/tex] to get the equation into slope-intercept form:
[tex]\[
y = 3x + 6 + 2
\][/tex]
Add the constants on the right-hand side:
[tex]\[
y = 3x + 8
\][/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]\[
y = 3x + 8
\][/tex]
So, the answer is:
[tex]\[
y = 3x + 8
\][/tex]
