Does the equation x^2 -4x + y^2 = -3 intersect the x-axis?
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Hello! Your answer is y = -7/3x + 2.
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First, find the slope of the original line. The slope can be calculated by . Substitute in the points, and you get:
So now we get: slope = 3/7. We do not need the full equation of the first line, as a perpendicular line only requires the slope.
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Perpendicular lines all have a slope that is a negative reciprocal of another. For example, if one line's slope was 1/4, the line perpendicular to it would have a slope of -4.
The negative reciprocal of 3/7 is -7/3. Therefore, we know the slope of the line that we are looking for is -7/3. We can substitute this into y = mx + b.
y = -7/3x + b
Now, we are given a coordinate point. Substitute that in and solve.
-5 = -7/3 * 3 + b
-5 = -7 + b
b = 2
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Therefore, the final equation we are looking for is y = -7/3x + 2.
Hope this helps!