Q.Find the equation of the line through $(-2, 3)$ with slope $-4$.

Concept: Slope Calculation — the slope-intercept form $y = mx + c$ gives the equation directly when the slope $m$ and a point are known.

Step 1: Start with $y = mx + c$. Here $m = -4$, so $y = -4x + c$.

Step 2: Substitute the point $(-2, 3)$:

$3 = -4(-2) + c \implies 3 = 8 + c$. …

Why point-slope form?

When you know a line’s slope and one point it passes through, you can immediately write its equation. The slope tells you how the line tilts — for every 1 unit you move right, you move $m$ units up (or down if $m$ is negative). The point anchors the line at a specific location.

The point-slope formula $y - y_1 = m(x - x_1)$ is just a direct translation of that idea: the vertical change from the known point equals the slope times the horizontal change. No memorisation of intercepts needed.

Step-by-step

1. Identify the given values.

   The point is $(-2, 3)$, so $x_1 = -2$ and $y_1 = 3$. The slope is $m = -4$.

2. Plug into the point-slope form.

Notice the double negative: $x - (-2)$ becomes $x + 2$.

3. Simplify the right-hand side.

Distribute the $-4$:

4. Solve for $y$ to get slope-intercept form. Add 3 to both sides: …