Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form.
line y+2= 0, point (1,−4)
y + 2 = 0,
Y = -2. This is a hor. line.
Slope = 0.
The perpendicular line is a ver. line:
X = 1 for all values of Y.
To find the equation of a line perpendicular to the given line, we need to first determine the slope of the given line.
The given line is y + 2 = 0. We can rearrange this equation to be in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
y + 2 = 0 can be rewritten as y = -2.
Since the slope of this line is -2, the slope of any line perpendicular to it will be the negative reciprocal of -2, which is 1/2.
Now that we have the slope and a point (1,-4) that the perpendicular line should pass through, we can use the point-slope form (y - y₁ = m(x - x₁)) to find the equation of the line.
Plugging in the values, we have:
y - (-4) = 1/2(x - 1)
Simplifying, we get:
y + 4 = 1/2x - 1/2
We can rewrite this equation in slope-intercept form (y = mx + b):
y = 1/2x - 1/2 - 4
y = 1/2x - 4.5
Therefore, the equation of the line perpendicular to y + 2 = 0 and passes through the point (1,-4) is y = 1/2x - 4.5.