Final answer:
To find the equation of a line that is perpendicular to a given line and passes through a point, you need to find the negative reciprocal of the slope of the given line. Using the point-slope form of a linear equation, you can then plug in the values to find the equation of the perpendicular line. In this case, the equation is y = 3x - 5.
Step-by-step explanation:
To find an equation for a line that is perpendicular to the given line and passes through a given point, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal of a slope 'm' is equal to -1/m.
First, let's find the slope of the given line using the formula: slope = (change in y) / (change in x).
Given points: (-3, 2) and (0, 1)
Slope = (1 - 2) / (0 - (-3)) = -1 / 3
So, the slope of the given line is -1/3. To find the equation of the line perpendicular to this, we take the negative reciprocal of -1/3, which is 3.
Now, we have the slope of the perpendicular line, and we have a point that lies on the line, which is (3, 4). We can use the point-slope form of a linear equation to find the equation of the line: y - y1 = m(x - x1).
Plugging in the values, we get: y - 4 = 3(x - 3)
Expanding and rearranging the equation, we have y = 3x - 5.