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:

$y=-\frac{7}{3}x-7$

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:

$y=-\frac{7}{3}x+b$

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

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

Thus, the equation of Line "l" is:

$y=-\frac{7}{3}x-4$