Question

Which best describes the graph of the line that has slope of -2/5 and passes through (10, -2) and the line that passes through (0,1) and (5,-1)?

A) coincident lines
B) intersecting lines
C) parallel lines
D) vertical lines

Answer 1

The line with a slope of -2/5 and passing through (10,-2) can be expressed in point-slope form as:

y - (-2) = (-2/5)(x - 10)

Simplifying this equation gives:

y = (-2/5)x + 2

The line passing through (0,1) and (5,-1) can be expressed in slope-intercept form as:

y - 1 = [-1 - 1]/[5 - 0](x - 0)

Simplifying this equation gives:

y = -0.4x + 1

Since the two lines have different slopes (-2/5 and -0.4), they are not parallel. To determine if they intersect, we can set the two equations equal to each other and solve for x:

(-2/5)x + 2 = -0.4x + 1

0.2x = 1

x = 5

Substituting x = 5 into either equation gives:

y = (-2/5)(5) + 2 = 0

Therefore, the two lines intersect at the point (5,0), and the answer is B) intersecting lines.