To write the equation of a line given a point and a slope, you can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is the point on the line and \(m\) is the slope.
For the point \((-3, -2)\) and the slope \(1\):
- \(x_1 = -3\)
- \(y_1 = -2\)
- \(m = 1\)
Substituting these values into the point-slope equation:
\[ y - (-2) = 1(x - (-3)) \]
This simplifies to:
\[ y + 2 = 1(x + 3) \]
Now, distribute the slope:
\[ y + 2 = x + 3 \]
Subtract \(2\) from both sides to put it into slope-intercept form:
\[ y = x + 3 - 2 \] \[ y = x + 1 \]
So, the equation of the line through the point \((-3, -2)\) with slope \(1\) is:
\[ y = x + 1 \]