Question

Given the equation y = 3x + 5 , write the equation of a new line that would have the same y-intercept but would be steeper.

Answer 1

Answer: y = 4x + 5

Step-by-step explanation:

The general equation of a line is y = mx + d ,

m = slope

d indicates the y-intercept, when x=0 , Y=5 => (0,5)

In the given line m = 3 , so that is the slope.

This slope has an angle = arctan(3) = 71.56º

If we need a steeper line, we have to increase m,

By example y = 4x + 5 , would have the same y-intercept but would be steeper.

This new line has a greater slope, with an angle = arctan (4) = 75.96º

Answer 2

Answer: y = 4x + 5

Explanation:

The general equation of a line is y = mx + d ,

m = slope

d indicates the y-intercept, when x=0 , Y=5 => (0,5)

In the given line m = 3 , so that is the slope.

This slope has an angle = arctan(3) = 71.56º

If we need a steeper line, we have to increase m,

By example y = 4x + 5 , would have the same y-intercept but would be steeper.

This new line has a greater slope, with an angle = arctan (4) = 75.96º

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