Section 3.5 Writing Equations of Lines 253 Student Check 2 Write the equation of the line that has the given slope and passes through the given point. Write the answer in both slope-intercept form and standard form. a. m = -5; (3, 1) b. m=- 2 7 ; (4, 5) c. m = 0; (-6, 9) d. undefined slope; (8, 1) ��������: Using method 1 or 2 produces the same linear equation. When using the slope-intercept form, we must substitute the values of m and b into y = mx + b to obtain the equation. When using the point-slope form, the equation is obtained through the process. Use Two Points to Write the Equation of a Line In Objectives 1 and 2, we were given the slope and a point on the line. If we know only two points on the line, we can still apply the two methods discussed earlier to write the equation of the line through these points. The only difference is that now we will have to calculate the slope of the line using the slope formula. Once the slope is known, we can use method 1 or method 2 to write the equation of the line. ���������������������� Writing the Equation of a Line Given Two Points Step 1: Find the slope of the line using the slope formula, m = y2 - y1 x2 - x1 . Step 2: Use the slope and one of the given points to find the equation of the line using either the slope-intercept form of a line or the point-slope form of a line. �� ������������������������ ������������������ Write the equation of the line, in slope-intercept form, that passes through the given points. 3a. (4, -3) and (-2, 9) 3b. (-4, 0) and (4, 12) 3c. (-2, 4) and (-2, 11) Solutions 3a. Find the slope of the line. m = y2 - y1 x2 - x1 State the slope formula. m = 9 - (-3) -2 - 4 Let (x1, y1) = (4, -3) and (x2, y2) = (-2, 9). m = 12 -6 Simplify numerator and denominator. m=-2 Simplify result. Use the point-slope form of a line to write the equation. Either of the given points can be used in the point-slope form as shown. m = -2, (x1, y1) = (4, -3) y - y1 = m(x - x1) y - (-3) = -2(x - 4) y + 3 = -2x + 8 y + 3 - 3 = -2x + 8 - 3 y = -2x + 5 m = -2, (x1, y1) = (-2, 9) y - y1 = m(x - x1) y - (9) = -2x - (-2) y - 9 = -2(x + 2) y - 9 = -2x - 4 y - 9 + 9 = -2x - 4 + 9 y = -2x + 5 Objective 3 ▶ Write the equation of a line given two points.
hendricks_beginning_algebra_1e_ch1_3
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