Answer: y=(1/2)x - 1
Explanation:
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
Let's start by finding the slope of the given line 2x + y = 3. To do this, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope:
2x + y = 3
y = -2x + 3
From this equation, we can see that the slope of the given line is -2.
Next, we need to find the negative reciprocal of -2 to find the slope of the line perpendicular to it. The negative reciprocal of a number is the negative value of its reciprocal. So, the negative reciprocal of -2 is 1/2.
Now that we have the slope of the line perpendicular to the given line, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (-2, -2). The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the coordinates of the given point and m represents the slope of the line.
Plugging in the values, we have:
y - (-2) = (1/2)(x - (-2))
y + 2 = (1/2)(x + 2)
Simplifying the equation, we get:
y + 2 = (1/2)x + 1
y = (1/2)x - 1
Therefore, the equation of the line passing through the point (-2, -2) and perpendicular to the line 2x + y = 3 is y = (1/2)x - 1.
I hope this helped :)