Write a linear equation for the line that passes through the point (−1, 7) and has slope m = −4.

Step-by-step solution

1. 1

   Choose the form that uses a point and a slope directly. Point-slope form is built for exactly this data:

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

   where $(x_1, y_1)$ is the known point and $m$ the slope. Nothing has to be solved for first.

2. 2

   Substitute, and handle the negative x-coordinate carefully. With $(x_1, y_1) = (-1, 7)$ and $m = -4$:

   $y - 7 = -4\bigl(x - (-1)\bigr) = -4(x + 1)$

   The subtraction of a negative coordinate turns into addition. Writing $-4(x - 1)$ here is the most common slip and would give the wrong intercept.

3. 3

   Distribute the slope.

   $y - 7 = -4x - 4$

4. 4

   Isolate y to reach slope-intercept form. Adding $7$ to both sides:

   $y = -4x - 4 + 7 = -4x + 3$

   So the slope is $-4$ (as required) and the y-intercept is $3$.

5. 5

   Check that the original point satisfies the equation. Substituting $x = -1$:

   $y = -4(-1) + 3 = 4 + 3 = 7 \ \checkmark$

   The point lies on the line and the coefficient of $x$ is the given slope, so both conditions hold. In standard form the same line is $4x + y = 3$.