If line g passes through point (2, 2) and is perpendicular to the line h, then what is the equation of line g? With h passing through two points (1, 2) and (3, 6)
slope of line through the two points = (6-2)/(3-1) = 2
so the slope of your new line = -1/2
since the slopes must be negative reciprocals of each other.
new equation:
y = (-1/2)x + b
but (2,2) lies on this
2 = (-1/2)(2) + b
3 = b
y = (-1/2)x + 3
To find the equation of line g when it is perpendicular to line h, you need to use the slope-intercept form of a line, which is y = mx + b. In this form, "m" represents the slope of the line, and "b" represents the y-intercept.
Let's start by finding the slope of line h using the two given points (1, 2) and (3, 6). The slope (m_h) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m_h = (y₂ - y₁) / (x₂ - x₁)
Substituting the values, we have:
m_h = (6 - 2) / (3 - 1)
= 4 / 2
= 2
Since line g is perpendicular to line h, the slope of line g will be the negative reciprocal of the slope of line h. Therefore, the slope (m_g) of line g will be:
m_g = -1 / m_h
= -1 / 2
Now that we have the slope, we can proceed to find the equation of line g. Using the point (2, 2) on line g, we can substitute the coordinates (x, y) = (2, 2) and the slope (m_g = -1/2) into the slope-intercept form:
y = mx + b (slope-intercept form)
2 = (-1/2)(2) + b (substituting the given values)
2 = -1 + b
2 + 1 = b
3 = b
Therefore, the y-intercept (b) of line g is 3. Now we can write the equation of line g as:
y = -1/2x + 3
So the equation of line g is y = -1/2x + 3.