Find the equation of the line passing through the points 12

Find the equation of the line passing through the points (-1/2, 2) and (-1, 1/5). Write the equation in point-slope form, slope-intercept form, and standard form. B The slope is undefined, (a) Select the correct choice below and fill in any answer boxes within your choice. The equation of the line in point-slope form is y-2 = 18/5 (x+1/2). The slope is undefined (b) Select the correct choice below and fill in any answer boxes within your choice. The equation of the line in slope-intercept form is y = 18/5x + 19/5. The slope is undefined The equation of the line in standard from is

Solution

The point slope form of the equation of a line passing through the point (x₁ , y₁ ) and with slope m is (y-y₁ ) = m(x –x₁). Let the point slope form of the equation of the line passing through the points (-1/2, 2) and (-1,1/5) be (y-y₁ ) = m(x –x₁). Here, the slope of the required line is (2 -1/5)/[-1/2—(-1)] = (9/5)/(1/2) = 2*9/5 = 18/5. Also, x₁ = -1/2 and y₁ = 2. Therefore, the point slope form of the equation of the required line is y-2 =          (18/5)[ x –(-1/2)] or, y-2 = (18/5)(x +1/2). Also then , y = (18/5)x +(18/5)*(1/2 )+2 = (18/5)x +(9/5+2) or, y = (18/5)x +(19/5). This is the slope-intercept form of the equation of the line. Further, we have (18/5)x –y +19/5 = 0 so that , on multiplying both the sides by 5, we get 18x -5y +19 = 0 or, 18x-5y = -19. This is the standard form of the equation of the required line.