Algebra Honors ( Periods 5 & 6)

The Slope-Intercept Form of a Linear Equation 8-4

For every real number, the graph of the equation y = mx is the line that has slope m and asses thrugh the origin.

For all real numbers m and b, the graph of the equation

y = mx + b

is the line whose slop is m and whose y-intercept is b.

This is called the slope intercept form of an equation of a line.

Find the slope and y-intercept of

We know m = 3/5 and b = 2

so the slope is 3/5and the y-intercept is 2

 Using only the slope and y-intercept to graph

The slope = -3/4 and the y-intercept is 6

Since the y-intercept is 6 you plot (0, 6)

Since the slop is -3/4 move 3 units down and 4 units to the right to locate a second point.

Draw the line between the two points and write the equation of the line directly above the line.

(Check our textbook)

Use only the slope and y-intercept to graph

2x – 5y = 10

Solve for y to transform the equation into the form y = mx + b

2x -5y = 10

-5y = -2x + 10

the slope is 2/5 and the y intercept is -2

Since the y intercept is -2, plot ( 0, -2)

Since the slope is 2/5 move 2 units up and 5 units to the right to locate the second point. Draw the line through the two points and write the equation directly above the line.

SEE TEXBOOK for the accurate graph

Lines in the same plane that do not intersect are PARALLEL.

Different lines with the same slope are parallel

Parallel lines that are not vertical have the same slope.

Show that the lines whose equations are 2x + y = 8 and y = -2x + 6 are parallel

write each equation in slope-intercept form

2x + y = 8 becomes y = -2x + 8

and the 2^nd one is y - -2x + 6

Slope of both is -2

Since both lines have the same slope AND different y–intercepts, they are parallel.

Perpendicular Lines

Any two lines that intersect to form right angles are perpendicular. 

In a plane, two lines that are not horizontal or vertical are perpendicular if and only if the product of their slopes is -1.

In a plane vertical lines and horizontal lines are perpendicular.

Show that the graphs of the following lines  are perpendicular

Write 6y + 8x = 7 in slope intercept form

The slope is -4/3

The slope of the first equation is ¾

(3/4)(-4/3) = -1

Therefore the lines are perpendicular

What about y = x + 6

and y = -x +4

they are perpendicular because (1)(-1) = -1