Question

A line that goes through the origin and the point (10,5).

a) y = 2x
b) y = 1/2x
c) y = 3x
d) y = 5x

Answer 1

b) y = 1/2x

Explanation:

Since it goes through the origin (0, 0), we already have two points and just have to plug them into the rise over run value. It goes up 5 units and moves 10 units to the right, so it could be written as:

5/10

Simplified, it's 1/2

Answer 2

The correct equation for the line that passes through the origin and point (10,5) is y = 1/2x, as it has a slope of 1/2 when the rise is 5 and the run is 10.

To find which equation represents the line that goes through the origin and the point (10,5), we need to calculate the slope of the line. The slope (m) of a line is calculated by the rise over the run, which is the change in y divided by the change in x. Since the line goes through the origin (0,0) and the point (10,5), the rise is 5 and the run is 10, resulting in a slope of 5/10 or 1/2.

From the options provided, the equation of the line with the slope of 1/2 is y = 1/2x. Since the line goes through the origin, the y-intercept (b) is 0, which matches the equation form y = mx + b with a y-intercept of 0. Therefore, the correct answer is b) y = 1/2x.