Question

What is the equation of the line that is parallel to the given line and has an x-intercept of â€""3? y = Two-thirdsx 3 y = Two-thirdsx 2 y = Negative three-halvesx 3 y = â€""Three-halvesx 2.

Answer 1

Equation of the line is the way to represent the line in the linear equation form by the given set of the points in the graph.The correct equation for the given problem is,

$y=\dfrac{2}{3}x +2$

Given-

Required equation is parallel to the given line and has an x- intercept of -3.

In the graph given the two point shown are (0,-1) and (3,1).

Equation of the line

Equation of the line is the way to represent the line in the linear equation form by the given set of the points in the graph.

Here in these points the value of x changes 3 with the change in y is 2.

Thus change in y to change in x is 2/3, which is the slope of the given line. Thus slope of the given line is 2/3.

The equation the line x with b as the intercept of y and the m as the slope of the line, can be given as,

$y=mx+b$

As the y intercept of the given line is -3.

Thus the value of b is -3. Put the value of m and b in the above equation to solve it further,

$y=\dfrac{2}{3}x -3$

Now as the line is parallel, this will need to have the same slope. At x-intercept of (-3,0) y is zero.

Put this values in above equation to solve further,

$0=\dfrac{2}{3}\times(-3) -b$

$b=-2$

With this value of b we get,

$y=\dfrac{2}{3}x +2[$

Thus, the correct equation for the given problem is,

$y=\dfrac{2}{3}x +2$

For more about the lines follow the link below-https://brainly.com/question/19300779