write an equation in slope intercept form of the line that passses through the given point and is parallel to the graph of the given equation
(2,-2) ;y=-x-2
Since it is parallel, the new equation must look like
y = -x + b, (it would differ only in the constant)
but (2,-2) lies on this line, so
-2 = -(2) + b
b = 0
new equation :
y = -x
Parallel lines have the same slope.
So, you want a line with slope = -1
Now you have a point and a slope. Use that to get
y+2 = -1(x-2)
y+2 = -x+2
y = -x
Or, given y = -x-2, you know that any parallel line will be y = -x + b
So, plug in x=2 into your equation, and you have
y = -2-2 = -4
But, you want y = -2, which is 2 units above that line. So, your final line is
y = -x-2+2 = -2x
To find an equation in slope-intercept form that passes through the point (2,-2) and is parallel to the given equation y=-x-2, we need to determine the slope of the given equation first.
The given equation is in the form y = mx + b, where m represents the slope.
Comparing the given equation y = -x - 2 with the slope-intercept form, we see that the slope (m) is -1.
Since parallel lines have the same slope, the equation we are looking for will also have a slope of -1.
Now, we can use the point-slope form of a linear equation to write the equation. The point-slope form is:
y - y1 = m(x - x1)
Substituting the values: (x1, y1) = (2, -2) and m = -1, we have:
y - (-2) = -1(x - 2)
Simplifying:
y + 2 = -x + 2
Rearranging the equation to the slope-intercept form (y = mx + b):
y = -x + 2 - 2
y = -x
So, the equation of the line passing through the point (2, -2) and parallel to the graph of y = -x - 2 is y = -x.
To write an equation in slope-intercept form (y = mx + b) for the line that passes through the point (2,-2) and is parallel to the graph of the equation y = -x - 2, we need to find the slope (m) of the given equation and then substitute the slope and the given point into the slope-intercept form.
The slope-intercept form equation y = mx + b represents a line, where "m" is the slope of the line and "b" is the y-intercept (the point where the line crosses the y-axis).
Given equation: y = -x - 2
The slope of this equation can be found by looking at the coefficient of x. In this case, the coefficient of x is -1. So, the slope (m) of the given equation is -1.
Since the line we want to find is parallel to this given line, the slope of the line we want to find will also be -1.
Now, we have the slope (m = -1) and the given point (2, -2). We can substitute these values into the slope-intercept form equation y = mx + b and solve for b.
Using the point-slope form: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we have:
y - (-2) = -1(x - 2)
y + 2 = -x + 2
y = -x + 2 - 2
y = -x
Therefore, the equation in slope-intercept form of the line that passes through the point (2,-2) and is parallel to the graph of the given equation y = -x - 2 is y = -x.