SOLUTION: Given 3x-5y+10=0, find the acute angle between the line and the y-axis, to the nearest degree.

Question 1100165: Given 3x-5y+10=0, find the acute angle between the line and the y-axis, to the nearest degree.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
start with 3x - 5y + 10 = 0

add 5y to both sides of the equation and flip sides to get:

you can flip sides because a = b is the same as b = a.

5y = 3x + 10

divide both sides of the equation by 5 to get:

y = 3/5 * x + 2

this is the slope intercept form of the equation of a straight line.

the slope is the change in y divided by the change in x.

what this says is that y goes up 3 when x goes to the right 5.

this forms a right triangle with the side opposite the angle = 3 and the side adjacent to the angle = 5.

what this says is that tangent of the angle is equal to 3/5.

solve for the angle to get the angle = arctan(3/5) = 30.96375653.

this can be rounded to 31 degrees.

this is the angle that the line makes with the x-axis.

the angle that the line makes with the y-axis is 90 - 30.96375653 = 59.03624347 degrees.

this can be rounded to 59 degrees.

here's what the line looks like on a graph.

$$$

what is shown on the graph is the equation of y = 3/5 * x.

this forces the y-intercept to be at the origin, so you can see the angle that the line makes with the x-axis and the y-axis more clearly.

y = 3/5 * x + 2 would intersect with the y-axis at y = 2.

taking the 2 away forces the line to intersect with the y-axis at the origin.

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