Question

The location of highway A is shown on the coordinate plane below.



Two additional highways are planned. Each will pass through the point (0,1) on the coordinate plane.

Highway B is to be parallel to Highway A.

Highway C is to be perpendicular to Highway A.

Which equations could describe either of those highways? Choose all that are correct.

(2 points)
Responses

y=54x+1

y is equal to 5 fourths x plus 1

y=−54x+1

y is equal to negative 5 fourths x plus 1

y=−45x+1

y is equal to negative 4 fifths x plus 1

y=45x+1

Answer 1

I can't see the diagram you mention. To pick the correct equations I need the slope of highway A from the graph.

How to choose once you know A's slope m:
- The line through (0,1) parallel to A has slope m, so equation y = m x + 1.
- The line through (0,1) perpendicular to A has slope −1/m, so equation y = −(1/m) x + 1.

From the answer choices (interpreting 54 as 5/4 and 45 as 4/5):
- If slope of A is 5/4, pick: y = 54x + 1 and y = −45x + 1.
- If slope of A is 4/5, pick: y = 45x + 1 and y = −54x + 1.

If you upload or describe two clear points on highway A from the graph (for example "A passes through (−5,−4) and (0,1)"), I will identify the correct pair.