Graph a linear equation

Graph: 2x – 3y = -12 - 3y = -2x – 12 2 y = x + 4 3 Solve for y so the equation looks like y = mx + b Subtract 2x to both sides.

Divide by –3 to both sides.

Now we can choose values for x to find values for y. X Y 3 0 -3 6 4 2 2 y = 3 (-3) + 4 2 y = (3) 2 y = (0) 3 3 + 4 + 4 PLOT y = 2 + 4 y = 4 y = -2 + 4 y = 2 NOW GRAPH A LINE y = 6

Graph a linear equation

Graph: 3x – 4y = 8 - 4y = -3x + 8 3 y = x – 2 4 Solve for y so the equation looks like y = mx + b Subtract 3x to both sides.

Divide by –4 to both sides.

Now we can choose values for x to find values for y. X Y 4 0 -4 1 -2 -5 3 y = 4 (-4) - 2 3 y = (4) 3 y = (0) 4 4 -2 - 2 PLOT y = 3 - 2 y = -2 y = -3 - 2 y = -5 NOW GRAPH A LINE y = 1

Graph a linear equation

Graph: 3x = 6 X = 2 Missing a y term, so solve for x Divide by 3 Now we can graph a line in which the value for x is 2 in all coordinates.

Notice the line is vertical because every coordinate on the line has an x coordinate of 2.

(2, 6) (2, 0) (2, -5)

Graph a linear equation

Graph: -4y = 12 Y = -3 Missing a x term, so solve for y Divide by -4 Now we can graph a line in which the value for y is -4 in all coordinates.

Notice the line is horizontal because every coordinate on the line has a y coordinate of -4.

(-3, -4) (0, -4) (3, -4)

Graph a linear equation using x and y intercepts.

Graph: 2x – 3y = -12 2 (0) – 3y = -12 0 - 3y = -12 -3y = -12 y = 4 Let x = 0 Now let y = 0 2x – 3 (0) = -12 2x – 0 = -12 2x = -12 x = -6 x intercept is (-6, 0) y intercept is (0, 4) PLOT NOW GRAPH A LINE

Graph a linear equation using x and y intercepts.

Graph: -5x + 3y = -15 -5 (0) + 3y = -15 0 + 3y = -15 3y = -15 y = -5 Let x = 0 Now let y = 0 -5x + 3 (0) = -15 -5x + 0 = -15 -5x = -15 x = 3 x intercept is (3, 0) y intercept is (0, -5) PLOT NOW GRAPH A LINE

Graph a linear equation, by using y intercept and slope.

Graph: 2x – 3y = -12 - 3y = -2x – 12 2 y = x + 4 3 Solve for y so the equation looks like y = mx + b Subtract 2x to both sides.

Divide by –3 to both sides.

Now the equation is in y = mx + b form called slope y-intercept form. 2 m is the slope of the line and b is the y-intercept (0, 4) Now plot the y-intercept (0, 4) 2 The slope of the line is so from the coordinate (0, 4) 3 go up 2 lines, then move right 3 lines and plot a 2 nd point.

UP 2 RIGHT 3

NOW GRAPH A LINE

Graph a line given one point and the slope of the line.

Graph the line that passes through the point (-4, 5)  5 3 slope of . and has a Plot the point (-4, 5)  3 Now from the point (-4, 5) the slope is , 5 so go down 3 lines and then right 5 lines. DOWN 3

Now graph the line

RIGHT 5