Answer:
The equation in slope-intercept form of the line that passes through(6,−11) and is parallel to the graph of y = −x2/3+ 12. is [tex]y=-\frac{2}{3}x-7[/tex]
Step-by-step explanation:
We need to Write the equation in slope-intercept form of the line that passes through(6, −11) and is parallel to the graph of y = −x2/3+ 12.
The general equation of slope-intercept form is: y=mx+b
where m is slope and b is y-intercept.
Since both the lines are parallel so, they have same slope. (If 2 lines are parallel they have same slope)
So, slope for our equation will be -2/3 (Taken from the equation of line given y=-2/3x+12 and comparing it with general form y=mx+b the value of m is -2/3 )
Now, we need to find y-intercept using point (6,-11) and slope m= -2/3
We will use equation: y=mx+b
Putting values:
[tex]y=mx+b\\-11=-\frac{2}{3}(6)+b\\-11=-2(2)+b\\-11=-4+b\\b=-11+4\\b=-7[/tex]
So, value of b is -7
Now, the equation of required line having slope = -2/3 and b=-7 is:
[tex]y=-\frac{2}{3}x-7[/tex]
The equation in slope-intercept form of the line that passes through(6,−11) and is parallel to the graph of y = −x2/3+ 12. is [tex]y=-\frac{2}{3}x-7[/tex]
