write an eaguation in slop-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
8.)2,-2;y=-x-2
parallel, same slope
y= -x+b
thru the point 2,-2
-2=-(2)+b
b=0
line is y=-x
Thanks!!
Use the point-slope form to write an equation of the line with the given slope and point.
m = 4, passes through (4, 6)
To write the equation of a line in slope-intercept form, you need to know the slope (m) and the y-intercept (b). In this case, you already have the equation of a line (y = -x - 2) and a point (2,-2) that the desired line passes through.
First, let's find the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. In the given equation, the coefficient of x is -1, so the slope is -1.
Since the desired line is parallel to the given line, they will have the same slope. So, the slope of the desired line is also -1.
Now, let's use the point-slope form of a line to find the equation of the desired line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Substituting the values into the point-slope form, we have:
y - (-2) = -1(x - 2)
Simplifying:
y + 2 = -x + 2
Rearranging the equation to the slope-intercept form, we get:
y = -x + 2 - 2
y = -x
Therefore, the equation of the line that passes through the point (2,-2) and is parallel to the graph of y = -x - 2 is y = -x.