Math coordinate graphing and solving systems of equations

Write an equation for the line that is parallel to y=3x + 1 (Given Line) and passes through (-4, 5). 1) graph the given line 2) graph the line parallel to the given line 3) find the equation of the parallel line

Answer: y = 3x + 17 or y-5 = 3(x+4) ---------------------------- y = ax + b the a is the slope, and it will be the same for parallel lines. the b is the value of y when x=0. See picture for graph. The given line is in blue, the parallel line is in purple. Given line: y = 3 x + 1 So the parallel line must be y = 3x + b Also, can plug in (-4, 5) -5 = 3 (-4) + ? -5 = -12 + ? ? = 17 so we know the parallel line is y = 3x + 17 we can also graph but draw the point at (-4, 5), and then draw the line so that the slope goes up 3 and over 1 (the slope is change in y over change in x--rise over run.)

. Answer: no, the slope of the lower line is -5/4, and the slope of the first line is -1. ------------------------------ First line is negative slope. two points they give are (-4,0) and (-1,-4) Calculate change in y over change in x: (-4-1) / (0-4) =-5/-4 First line also ngative slope. two points they give are (0,5) and (4,1) change in y over change in x: (0-4) / 5-1 =-4/4 = -1 The slopes are different

Are the lines parallel, perpendicular, or neither? Prove showing their slopes

What is the solution of the system? Find with a graph. y = -4x + 1 y = x-4

Solution is (1, -3)

answer: y = -1/3 x - 2 ---------------------------------------- y = ax + b a is the slope the line goes up 1 and over to the left 3 it is negative (slanting down to the right) so the slope is 1/3 the b is the value of y when x=0 it is -2 So the equation is y = -1/3 x - 2

What is the equation of the graph?

Write an equation for the line that is perpendicular to y = 2/3*x - 5 and passes the (1, -2) 1) graph the given line 2) graph the line perpendicular to the given line 3) find the equation of the given line

answer: y = -3/2 x + 1/2 or 2y = -3x + 1 or y + 2 = -3/2 (x-1) see image (blue line is given line; purple line is perpendicular line) ------------------------------------ we know the slope of the given line is 2/3 so the slope of a line perpendicular to it is the negative reciprocal of that . It is -3/2 y = -3/2 x + ? Plug in (1, -2) -2 = -3/2 (1) + ? ? = -2 + 3/2 = -4/2 + 3/2 = 1/2 the line is y = -3/2 x + 1/2 or (if you multiply both sides by 2) 2y = -3x + 1

What is the solution to the system? Use elimination. 2x - 2y = -8 x + 2y = -1

answer: (-3, 1) 2x - 2y = -8 x + 2y = -1 add the equations together 2x + x = 3 x -2y + 2y = 0 -8 - 1 = -9 3x = -9 x = -3 then substitute x into equation 2*(-3) - 2y = -8 -6 - 2y = -8 -2y = -8 + 6 -2y = -2 y = 1

What is the solution of the system? Use substitution. 3x + 2y = 7 y = -3x + 11

answer: (5, -4) 3x + 2y = 7 y = -3x + 11 substitute in for y: 3x + 2(-3x + 11) = 7 multiply each term in parentheses by 2 3x - 6x + 22 = 7 subtract 22 from each side 3x - 6x = -15 then combine the x terms -3x = -15 divide each side by -3 x = 5 then plug in for first equation 3x + 2y = 7 3(5) + 2y = 7 15 + 2y = 7 2y = 7-15 2y = -8 y = -4