Question

Write the equation in slope-intercep tform of the line that passes through(6, −11) and is parallel to the graph of y = −x2/3+ 12.

Answer 1

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
`y=-(2)/(3)x-7`

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:

`y=mx+b\\-11=-(2)/(3)(6)+b\\-11=-2(2)+b\\-11=-4+b\\b=-11+4\\b=-7`

So, value of b is -7

Now, the equation of required line having slope = -2/3 and b=-7 is:

`y=-(2)/(3)x-7`

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
`y=-(2)/(3)x-7`