Question

Which line has a slope of 0.625, and which line has a slope of 1.6?

Explain why the slopes of these lines are 0.625 and 1.6.

Answer 1

The answer is below

Explanation:

The equation of a straight line is given by:

y = mx + b; where y and x are variables, b is the y intercept (i.e. value of y when x is zero), m is the slope of the line.

The slope of a line passing through the points
`(x_1,y_1)\ and\ (x_2,y_2)\ is:`

`m=(y_2-y_1)/(x_2-x_1)`

Let the point where the two lines intersect be the origin (0, 0).

Line 1 passes through (0, 0) and (8, 5). Hence:

slope of line 1 =
`(y_2-y_1)/(x_2-x_1)=(5-0)/(8-0) =0.625`

Line 2 passes through (0, 0) and (5, 8). Hence:

slope of line 2 =
`(y_2-y_1)/(x_2-x_1)=(8-0)/(5-0) =1.6`