Write an equation of a line that passes through the point (2,0) and is perpendicular to the line y=−1/2x+3

Step-by-step explanation:

step 1

Find the slope of the given line

we have

This is the equation of the line in slope intercept form

The slope is

step 2

Find the slope of the line perpendicular to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

we have

----> slope of the given line

therefore

The opposite reciprocal is

step 3

Find the equation of the line in point slope form

we have

substitute

Convert to slope intercept form

see the attached figure to better understand the problem

there is no

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.