Which of the following is equivalent to the expression below?
(14 + 2x) - 2x

The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is: y=-x+3

Step-by-step explanation:

Given equation of line is:

Comparing it with the general form of equation of line in slope-intercept form

The slope of given line is 1 as the co-efficient of x in the equation is 1.

When two lines are perpendicular, the product of their slopes is -1

Let m1 be the slope of new line

Then

The equation of new line perpendicular to given line will be:

Putting the value of m1

To find the value of b, the given point will be put into the equation

So,

The final equation of line is: y = -x+3

Hence,

The equation in slope-intercept form through the point (4, -1) and is perpendicular to the line y = x + 2 is:

Graph:(Attached)

The graph is made using the online graphing tool "Desmos". The red line in the graph represents the line y = x+2 and the blue line represents the line (y=-x+3) perpendicular to given line