Gien the points (3,-1) and (-1,1)

Question

a. What is the slope (m)?

b. Find the y-interept (b).

c. What is the equation of this line?

d. Find the equation of a line perpendicular to this one through the point (1,1)

e. Graph both lines

Answer 1

The slope of the line is (1 - (-1))/(-1 - 3) = 2/(-4) = -1/2

 

We can use the point-slope form of the equation of a line, which is y - y₀ = m(x - x₀) to obtain y - 1 = -1/2 (x + 1). Recall that m = slope and (x₀, y₀) is a point on the line.

 

y - 1 = -1/2 x - 1/2

y = -1/2 x + 1/2

 

To find the y-intercept, we know that y = mx + b is the slope-intercept form of the equation of a line. Here, b = 1/2, and b corresponds to the y-intercept. In other words, when x = 0, y = 1/2, and the graph of the line intersects the y-axis at the point (0, 1/2).

 

The line perpendicular to this line will have the negative reciprocal slope. The negative reciprocal of -1/2 is 2. If this perpendicular line passes thru (1, 1), then its equation is

 

y - 1 = 2(x - 1)

y - 1 = 2x - 2

y = 2x - 1

 

I will leave it to you to graph the two lines, as that is not possible on this platform.