Question

What is the equation of a line in point-slope form that passes through the point (-2, 14) and has a slope of:

a) 7
b) -5
c) -2
d) 23

Answer 1

The point-slope form equations for a line passing through the point (-2, 14) with slopes of 7, -5, -2, and 23 are y - 14 = 7(x + 2), y - 14 = -5(x + 2), y - 14 = -2(x + 2), and y - 14 = 23(x + 2) respectively.

Step-by-step explanation:

The point-slope form of the equation of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. For a line that passes through the point (-2, 14) and has different slopes, we can plug these values into the equation to get the specific equations for each given slope.

• For a slope of 7: y - 14 = 7(x + 2)
• For a slope of -5: y - 14 = -5(x + 2)
• For a slope of -2: y - 14 = -2(x + 2)
• For a slope of 23: y - 14 = 23(x + 2)

Each equation represents the respective line with a specific slope through the given point.