Question: Write the point-slope equation given a point and a slope.
Graph: a line with positive slope rising from bottom-left to top-right, passing through the labeled points $(0, -1)$ at the center area and $(4, 2)$ in the upper-right; position_hint = center.
$m =$
equation: = + +
1. **State the problem:** We need to find the point-slope form of the equation of a line given two points: $(0, -1)$ and $(4, 2)$.
2. **Recall the point-slope formula:** The point-slope form of a line is given by:
$$y - y_1 = m(x - x_1)$$
where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
3. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-1)}{4 - 0} = \frac{2 + 1}{4} = \frac{3}{4}$$
4. **Write the equation using point-slope form:** Using the point $(0, -1)$ and slope $m = \frac{3}{4}$:
$$y - (-1) = \frac{3}{4}(x - 0)$$
which simplifies to:
$$y + 1 = \frac{3}{4}x$$
5. **Final equation:**
$$y + 1 = \frac{3}{4}x$$
This is the point-slope form of the line passing through the given points with the calculated slope.