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Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
1. Lines in the Plane
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Exercise 1 Page 11

Recall the definitions of the form of equations.

(a) iii
(b) i
(c) v
(d) ii
(e) iv

We are given the following equations. &(a) Ax+By+C=0 &(b) x=a &(c) y=b &(d) y=mx+b &(e) y-y_1 = m(x-x_1) We want to match each of these equations with its form. (i)& vertical line (ii)& slope-intercept form (iii)& general form (iv)& point-slope form (v)& horizontal line Let's recall the definition of each form of equations.
Form of Equations Definition
(i) vertical line A line with undefined slope is vertical. It always intersect the x-axis at a point a and expressed as x=a.
(ii) slope-intercept form The slope-intercept form of the equation of the line that has a slope of m and y-intercept of (0,b) is y=mx+b.
(iii) general form The general form of the equation of a line is Ax+By+C=0, where A, B, and C are constants.
(iv) point-slope form The point-slope form of the equation of the line that passes through the point (x_1,y_1) and has a slope of m is y-y_1 = m(x-x_1).
(v) horizontal line A line with zero slope is horizontal. It always intersect the y-axis at a point b and expressed as y=b.

We can now match each equation with its form.

Equations Form of Equations
(a) Ax+By+C=0 (iii) general form
(b) x=a (i) vertical line
(c) y=b (v) horizontal line
(d) y=mx+b (ii) slope-intercept form
(e) y-y_1 = m(x-x_1) (iv) point-slope form
Subchapter links expand_more
arrow_right Vocabulary and Concept Check p.11
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arrow_right Procedures and Problem Solving p.11-14
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arrow_right Conclusions p.14-15
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arrow_right Cumulative Mixed Review p.15
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