Question

In problems 1 - 4, write the equation in the slope-intercept form using the given information. 1. Write the equation in the slope-intercept form that passes through the given point and has the indicated slope m. (3,-4) and m=- 2. Write the equation in the slope-intercept form that passes through the given points: (-1,-2) and (3,-4) 3. Write the equation in the slope-intercept form of the line that passes through the point (-1, 3) and is parallel to the line –2x+y=5. 4. Write the equation in the slope-intercept form of the line that passes through the point (2, -1) and is perpendicular to the line y=-x-4

Answer 1

11. Equation of line in slope-intercept form. is y=mxto - (1) where mis slope & cis intercept. Given, m= 1/2 so y = - 3 +C. the line passes through (3,-4) so 4= - +C = C = -4+3 (3) c= - 8 +3 = 5 Thus with value of m & c egn of line is, y = - 1 x + 5 = 1 2. Equation of line in slope intercept form is a y=mx+c (1) with slope m & intercept c. Line(1) passes through points (-1,-2) $ (3,-4) so -2=-mic - 4 = 3 m+c Egh (3) - Egh (2) gives 2+4 = - 400 2= - 4m m = -1 894 (2) with a gives -2=-1-2) + C Substituting value of m &c in egros, e c=-2-22 = - - - Y = -12 x - 5 This is required line. 3. Equation of line in slope - intercept form is y=mx+c-Owith Slope m & intercept C. Line (1) passes through point (+1, 3) so by egh (1) 3 - M+C - (2) Line (1) is parallel to dine –2x+y = 5 ore y=2x+5 so slope of line (1) & line 2

is same i.e. m = slope of (y= 2x+5) = 2x+5 1 y=mx+C m = 2 lequating n=2 Substituting value of m in egh (2) 3= -2 +C C=3+2 =5 Put value of m &c in earl) Y = 2x+5] This is required line. 7 Equation of line in slope intercept form is y=mxtc, with slopem & intercept c.. Line(1) passes through the point (2,-1) so = 2m + c – (2) Line (1) is perpendicular to line (3) 19 = 2 2 x 4 comparing with y=m'a tc) I gives slope m'= 2 / 2 so slope of line (1) x Slope of line (3)=-| | m < - - mx 2 =-1 [m=-2 / 1 from eah (2), 1 = 2 (-3) to C = 1+3 = 2 Putting value of m&c in equation (1) y=-3x+2 This is required equation of line.