Question

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Slope: 1/2, passing through the origin

Write an equation for the line in point-slope form.

A) y = 1/2x

B) y = -1/2x

C) y = 2x

D) y = -2x

Answer 1

The equation of a line with a slope of 1/2 that passes through the origin is y = (1/2)x. This equation is both the point-slope form and the slope-intercept form since the y-intercept is 0.

Step-by-step explanation:

The student is asking for the equation of a linear equation with a slope of 1/2 that passes through the origin. The point-slope form of the line's equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Since the line passes through the origin, which is the point (0, 0), we can substitute these values into the point-slope form equation. Therefore, the equation becomes y - 0 = (1/2)(x - 0), or simply y = (1/2)x.

In slope-intercept form, which is expressed as y = mx + b, where m is the slope and b is the y-intercept, the equation of the line is simply y = (1/2)x since the line passes through the origin and the y-intercept is 0.