To determine the equation of a line given the slope and a point it passes through, we can use the point-slope form of a line. This form is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
In this problem, we are given:
- The slope [tex]\( m = 3 \)[/tex]
- A point on the line, [tex]\((-2, -15)\)[/tex]
Substituting these values into the point-slope form, we have:
[tex]\[ y - (-15) = 3(x - (-2)) \][/tex]
Simplifying the equation:
[tex]\[ y + 15 = 3(x + 2) \][/tex]
Next, we distribute the slope (3) on the right-hand side:
[tex]\[ y + 15 = 3x + 6 \][/tex]
To isolate [tex]\( y \)[/tex], we subtract 15 from both sides:
[tex]\[ y = 3x + 6 - 15 \][/tex]
Combining the constants on the right side:
[tex]\[ y = 3x - 9 \][/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]\[ y = 3x - 9 \][/tex]
