Question

Given points P(5, 2) and Q(7, -5), write the equation of the line passing through these points.

a) y=−0.5x−3
b) y=−3.5x−15
c) y=5x+19
d) y= 1.25x + 4

Answer 1

To find the equation of the line passing through points P(5, 2) and Q(7, -5), we use the slope formula and point-slope form of a linear equation. we get the equation to be y = -3.5x + 15.5

Step-by-step explanation:

To write the equation of the line passing through points P(5, 2) and Q(7, -5), we first need to find the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the points, we get:
slope = (-5 - 2) / (7 - 5) = -7 / 2 = -3.5

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)

Substituting the slope and one of the points, we get:
y - 2 = -3.5(x - 5)

Simplifying the equation gives us:
y = -3.5x + 17.5 - 2
y = -3.5x + 15.5

So, the equation of the line passing through points P(5, 2) and Q(7, -5) is:
y = -3.5x + 15.5