To find the equation of the line passing through the points $(-2,3)$ and $(-1,4)$, we follow these steps:

Step 1: Find the Slope

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given points $(-2,3)$ and $(-1,4)$:

$m = \frac{4 - 3}{-1 + 2} = \frac{1}{1} = 1$

Step 2: Use Point-Slope Form

The equation of a line in point-slope form is:

$y - y_1 = m(x - x_1)$

Using the point $(-2,3)$:

$y - 3 = 1(x + 2)$

$y - 3 = x + 2$

Step 3: Convert to General Form

The general form of a line is:

$Ax + By + C = 0$

Rearranging $y - 3 = x + 2$:

$x - y + 2 + 3 = 0$

$x - y + 5 = 0$

Final Answer:

$x - y + 5 = 0$

Would you like a verification or graphical representation?

Related Questions:

1. How do you find the equation of a line given its slope and one point?
2. What is the meaning of slope in the context of linear equations?
3. How do you determine if two lines are parallel or perpendicular?
4. How do you find the distance between a point and a line?
5. How do you convert between slope-intercept form and general form?

Tip:

Always check your final equation by substituting the given points to ensure they satisfy the equation!