Find the equation of the line that is perpendicular to the line y =- 1/3 x-1 and passes through the point (1, 5)? justify how you knew what slope to use for step 1. show all work needed to complete this problem

To find the other line's slope, take the "opposite reciprocal"

For example, if the slope is -1/3, you change the negative sign to positive and you take the reciprocal.

-1/3 --> +3/1

The slope of the perpendicular will be positive 3. To find the equation that passes through the point (1,5), substitute the x and y values into the equation y=mx+b and solve for b, because you know the slope already, now you have to find the y-intercept (the b in the equation).

5=3(1)+b

5=3+b

5-3= 3-3+b

2=b

The equation of the perpendicular line is y=3x+2

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.