Find an equation of the line with the given slope of -7 that passes through the point (-3, -4)

We will use the concept of the point-slope form of a straight line to find the equation.

Answer: The equation of the line in slope-intercept form passing through the point P(-3, -4) with slope -7 is given as y = -7x - 25.

Let us see how we will use the concept of the point-slope form of the straight line to find the equation.

Explanation:

We will use the definition of slope to find the slope

Let us consider another point on the line that is (x, y).

We know that given two points (x₁, y₁) and (x₂, y₂) the slope is given by,

Slope(m) = (y₂ - y₁) / (x₂ - x₁)

Here, m = -7

Hence, the slope of the line passing through the points (-3, -4) and (x, y) is,

Slope =  (y + 4) / (x + 3) = -7

⇒ y + 4 = -7 (x + 3)

⇒ y - 4 = -7x - 21 

⇒ y = -7x - 21 - 4

⇒ y = -7x - 25

Thus, y = -7x - 25 is the equation of the required line.