Answer:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of a line that is perpendicular to y = (1/2)x - 3, we need to determine the slope of the perpendicular line.
The given line has a slope of 1/2. To find the slope of the perpendicular line, we can use the fact that the product of the slopes of two perpendicular lines is always -1.
The slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.
The negative reciprocal of 1/2 is -2. Therefore, the slope of the perpendicular line is -2.
Now, we have the slope (-2) and the point (-2, 2) that the line passes through. We can use the point-slope form of a line to find the equation.
The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Substituting the values into the point-slope form, we get:
y - 2 = -2(x - (-2))
Simplifying, we have:
y - 2 = -2(x + 2)
Expanding the equation, we get:
y - 2 = -2x - 4
To get the equation in slope-intercept form, we isolate y:
y = -2x - 2
Therefore, the equation in slope-intercept form of the line that passes through (-2, 2) and is perpendicular to the graph of y = (1/2)x - 3 is y = -2x - 2.