⧼exchistory⧽
9 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
[math]
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[/math]
For each of the following lines, find an equation that defines it.
- The line through [math](2,3)[/math] with slope [math]1[/math].
- The line through [math](0,1)[/math] with slope [math]1[/math].
- The line through [math](0,1)[/math] with slope [math]-2[/math].
- The line through [math](-1, -3)[/math] with slope [math]-\frac12[/math].
- The line through [math](-2, 1)[/math] and [math](-1,-1)[/math].
- The line containing the point [math](1, 0)[/math] and [math](0,1)[/math].
- The line through the origin containing the point [math](1, -19)[/math].
- The line with slope [math]0[/math] that passes through [math](3, 4)[/math].
- The line through [math](2, 5)[/math] and [math](2, 8)[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
Draw the line defined by each of the following equations, and find the slope.
- [math]x+y=1[/math]
- [math]x=-y[/math]
- [math]2x-4y=3[/math]
- [math]7x=3[/math]
- [math]7y=3[/math]
- [math]4x + 3y = 10[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
Determine whether [math]P[/math], [math]Q[/math], and [math]R[/math] lie on a line. If they do, draw the line and write an equation for it.
- [math]P = (0,0)[/math], [math]Q = (-1, 3)[/math], [math]R = (3, -4)[/math].
- [math]P = (\frac12,\frac32)[/math], [math]Q = (\frac52, -\frac72)[/math], [math]R = (-\frac32, -\frac{13}2)[/math].
- [math]P = (a_1,a_2)[/math], [math]Q = (b_1, b_2)[/math], [math]R = (c_1, c_2)[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
Draw the set of all ordered pairs [math](x,y)[/math] such that
- [math]4x^2 + 4xy + y^2 + 12x + 6y + 9 = (2x + y + 3)^2 = 0[/math].
- [math]5x^2 + 7xy + 2y^2 + 3x + 3y = (5x + 2y + 3)(x + y)= 0[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
The [math]x[/math]-coordinate of a point where a curve intersects the [math]x[/math]-axis is called an [math]x[/math]-intercept of the curve. The definition of a [math]y[/math]-intercept is analogous.
- Find the [math]x[/math]- and [math]y[/math]-intercept of the line defined by [math]y-3x=10[/math]. Draw the line.
- Write an equation for the line with slope [math]m[/math] and [math]y[/math]-intercept equal to [math]b[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
For each of the following equations, define the function [math]f(x)[/math] whose graph is the set of ordered pairs that satisfy the equation. Which ones are linear functions?
- [math]3x-y=7[/math]
- [math]5y=3[/math]
- [math]2|x| + 3y= 4[/math]
- [math]x-y=1[/math]
- [math]y^2 + 2x +3=0[/math] (two functions)
- [math]x^2 - 2xy + y^2 = 0[/math]
- [math]y = 3x^2 + 4x +2[/math]
- [math]5x + 3y = 1[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
Among the lines defined by the following equations, which pairs are parallel and which perpendicular?
- [math]4x + 2y = 13[/math]
- [math]3x - 6y = 0[/math]
- [math]3x + 2y = 6[/math]
- [math]y = -2x[/math]
- [math]4x = 13[/math]
- [math]4y = 13[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
- Write an equation of the straight line [math]L_1[/math] that contains the points [math](1,3)[/math] and [math](3, -2)[/math].
- Write an equation of the line with [math]x[/math]-intercept [math]1[/math] that is parallel to [math]L_1[/math].
- Write an equation of the line perpendicular to [math]L_1[/math] that passes through [math](1, 3)[/math].
BBy Bot
Nov 03'24
[math]
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[/math]
Prove that the two lines [math]L_1[/math] and [math]L_2[/math] in Figure are perpendicular. (Hint: Use congruent right triangles or the converse of the Pythagorean Theorem.)