Line w is parallel to line x and perpendicular to line y. Line y passes through the orgin and intersects line w at the point (10, 10). Line x has an x-intercept of 5. Find the equations of all three lines. Explain your reasoning
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Well, you have 2 points that are on line y. So you can use those two points to find the slope. And with the slope and one of the points you can get the equation for line y using the point slope formula.
Once you have the slope of line y you have the slope of line x because x is perpendicular to y. Therefore the slopes are negative reciprocals of each other. Knowing the slope of x and the x intercept of x, you have a point and a slope, and again can find the equation by plugging into point slope.
And once you have the slope of x you have the slope of w because they are parallel and have the same slope. You also have a point on w (10,10) which is where it intersects the line y. Therefore you can find the equation of w with point slope.
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Mkay, so how do I put those to points into an equation
So you just need 2 formulas, the formula for the slope of a line using 2 points on the line is:
And point slope formula for a line is
\[y-y_1 = m(x-x_1)\]
Where \(x_1, y_1\) are the x and y values for a point on the line and m is the slope.
Popak can you help me when you're done here please? sorry to interrupt