Section 2.3 Equations of a Line 165 Calculator Connections From Example 8, the line defined by should be perpendicular to the x 3 23 y 32 line y x 1 and should pass through the point (4, 3). Note: In this example, we are using a square window option, which sets the scale to display distances on the x- and y-axes as equal units of measure. y 23 x 1 y 32 x 3 3. Equations of a Line: A Summary Alinear equation can be written in several different forms,as summarized inTable 2-2. Table 2-2 Form Example Comments Standard Form Ax By C 2x 3y 6 y k y 3 x k x 2 y 2x 5 Slope 2 m 2 y mx b 1x1, y12 y y1 m1x x1 13, 12 2 1x1, y12 Although it is important to understand and apply slope-intercept form and the point-slope formula, they are not necessarily applicable to all problems. Example 9 illustrates how a little ingenuity may lead to a simple solution. Finding an Equation of a Line Find an equation of the line passing through the point (4, 1) and perpendicular to the x-axis. Solution: Any line perpendicular to the x-axis must be vertical. Recall that all vertical lines can be written in the form x k, where k is constant.A quick sketch can help find the value of the constant (Figure 2-25). Because the line must pass through a point whose x-coordinate is 4, the equation of the line is x 4. Skill Practice 11. Write an equation of the line through the point (20, 50) and having a slope of 0. Example 9 A and B must not both be zero. Horizontal Line The slope is zero, and the y-intercept (k is constant) is (0, k). Vertical Line The slope is undefined and the x-intercept (k is constant) is (k, 0). Slope-Intercept Form Solving a linear equation for y results in slope-intercept form.The coefficient of Slope is m. the x-term is the slope, and the constant y-Intercept is (0, b). y-Intercept is (0, 5). defines the location of the y-intercept. Point-Slope Formula This formula is typically used to build an Slope is m and equation of a line when a point on the is a point on the line. y 1 21x 32 line is known and the slope is known. y x (4, 1) 5 4 3 2 1 54321 1 2 3 4 5 1 2 3 4 x 4 5 Figure 2-25 Answer 11. y 50
miller_intermediate_algebra_4e_ch1_3
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