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.
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.