Concept Check Work each problem. Find the equation of the line...

Question

Concept Check Work each problem. Find the equation of the line that passes through the origin and makes a 30° angle with the x-axis.

Accepted Answer

Hello, everyone. We're asked to find the line that passes through the 0.60. We're told this line forms a 45 degree angle with a positive X axis. We want to determine the equation of the line in slope intercept form. Our answer choices are A Y equals X plus six by equals one half X plus six cy equals two X minus six, DY equals X minus six. So first I recall that slope intercept form is Y equals MX plus B where M stands for our slope and B stands for our Y intercept. And we are given a point, we're given the 0.60 that however, is an X intercept, not A Y intercept. So we'll save that and use that in a minute knowing that this line forms a 45 degree angle with a positive X axis. I can use the fact that slope will equal the tangent of 45 degrees to find the slope for this equation. So thinking about a unit circle, unit circles don't show me tangent. But what they do show me is sign and cosign. So I'm gonna say our slope is the sine of 45 degrees divided by the cosine of 45 degrees. Referencing a unit circle. I know that the sign of 45 degrees is radical two divided by two. So that's my numerator and I'm going to divide that by the cosine of 45 degrees, which is also radical two divided by two. So since I have radical two divided by two, divided by radical two divided by two, our slope equals one. So now we know the slope is one, we have a 0.60. So that's my X and my Y and I'm gonna use that in slope intercept form to find the equation of the line. First, I'm gonna find the Y intercept. So to find the Y intercept, I'm going to plug in X as 60 for Y and the slope as one. So I'll have zero equals the slope one multiplied by six, which is X plus B because that's my unknown. I'm looking for B which is the Y intercept. So I get zero equals six plus B. And when I saw for be I get that B equals negative six. So now knowing the slope is one, the Y intercept is negative six, I can plug that into Y inter um sorry slope intercept form. So Y will equal the slope one multiplied by X. So one X is X and the Y intercept is negative six. So we'll have it as minus six. So the equation of this line is Y equals X minus six which is answer choice. D have a nice day.

Concept Check Work each problem. Find the equation of the line that passes through the origin and makes a 30° angle with the x-axis.

Key Concepts

Slope of a Line from an Angle

Equation of a Line Through the Origin

Trigonometric Functions and Angle Measurement

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