Answer:
Therefore, the equation in slope-intercept form of the line that passes through the point (0,0) and is perpendicular to the graph of y = (1/2)x - 1 is y = -2x.
Explanation:
To find the equation of the line that passes through the point (0,0) and is perpendicular to the graph of the equation y = (1/2)x - 1, we need to determine the slope of the perpendicular line. The given equation is in slope-intercept form, y = mx + b, where m represents the slope of the line. In this case, the slope of the given line is 1/2. For lines that are perpendicular to each other, the slopes are negative reciprocals of each other. To find the slope of the perpendicular line, we take the negative reciprocal of 1/2: Negative reciprocal of 1/2 = -2/1 = -2 Now that we have the slope of the perpendicular line (-2), we can use the point-slope form of a linear equation to write the equation of the line. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. We can substitute the values (0,0) for (x₁, y₁) and -2 for m: y - 0 = -2(x - 0) Simplifying further, we get: y = -2x.