Question

Line k has the equation y= – 7/3x-7Line l is parallel to line k, but passes through the point (-2,2/3). Find an equation for line in slope-intercept form. An equation for l in slope-intercept form is: y=-7/3x+7

Answer 1

Equation of Line K:

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

The slope intercept form of a line is y = mx + b.

Equation of Line "l":

Line "l" and Line K are parallel. Line "l" will have the same slope.

It will be of the form:

`y=-(7)/(3)x+b`

It passes through the point (-2, 2/3). We plug the coordinates of "x" and "y" into the slope intercept form and find b:

`\begin{gathered} y=-(7)/(3)x+b \\ (2)/(3)=-(7)/(3)(-2)+b \\ (2)/(3)=(14)/(3)+b \\ b=(2)/(3)-(14)/(3) \\ b=-(12)/(3) \\ b=-4 \end{gathered}`

Thus, the equation of Line "l" is:

`y=-(7)/(3)x-4`