what is an equation of the line in point slope form that passes through the given point and has a given slope.(8,-8);slope 3. caon someone explain
having slope 3 means that for every point (x,y) on the line, measuring from (8,-8), the change in y over the change in x is 3.
in algebra, that means
(y-(-8))/(x-8) = 3
or
y+8 = 3(x-8)
Thank you for the help
Of course! To write the equation of a line in point-slope form, we need two pieces of information: the slope of the line and a point that it passes through.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point, and m is the slope.
In this case, the given point is (8, -8), and the slope is 3.
To find the equation, we can substitute these values into the point-slope form equation:
y - (-8) = 3(x - 8)
Simplifying:
y + 8 = 3x - 24
Now, we can rearrange the equation to isolate y:
y = 3x - 24 - 8
y = 3x - 32
Therefore, the equation of the line in point-slope form that passes through the point (8, -8) and has a slope of 3 is y = 3x - 32.