Question

through: (-3,-2), slope = 1

Answer 1

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:

\[
y = x + 1
\]