Objective graph linear equations using slope-intercept form.

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Presentation transcript:

Objective graph linear equations using slope-intercept form

Slope Review The slope m of a line passing through two points and is the ratio of the rise change to the run. y run rise x

Section 4.5 “Graph Using Slope-Intercept Form” a linear equation written in the form y-coordinate x-coordinate y = mx + b slope y-intercept

Identifying Slope and the Y-Intercept Slope of 3 means: y = 3x + 4 y = mx + b The equation is in the form y = m x + b. So, the slope of the line is 3, and the y-intercept is 4. 3x + y = 2 Rewrite the equation in slope-intercept form by solving for y. y = 2 – 3x Is this in slope-intercept form? The line has a slope of – 3 and a y-intercept of 2. y = -3x + 2

Identify the slope and y-intercept of the line with the given equation. 3x – 3y = 12 Rewrite the equation in slope-intercept form by solving for y. 3x – 12 = 3y Rewrite original equation. y 3x – 12 = 3 Divide 3 by equation. y x – 4 = Simplify. ANSWER The line has a slope of 1 and a y-intercept of –4.

Graph the equation y = 2 - 2x. Graph an Equation Using the Slope-Intercept Form Graph the equation y = 2 - 2x. y-axis 5 4 Rewrite in slope-intercept form 3 2 1 slope y-intercept -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x-axis Slope of -2 means: -1 -2 OR -3 Slope of -2 means: -4 -5

Graph the equation y = -3 + 2/3x. Graph an Equation Using the Slope-Intercept Form Graph the equation y = -3 + 2/3x. y-axis 5 4 Rewrite in slope-intercept form 3 2 1 slope y-intercept -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x-axis Slope of 2/3 means: -1 -2 OR -3 Slope of 2/3 means: -4 -5

Graph Using Slope and the Y-Intercept Graph the equation 2x + y = 3. STEP 1 Slope of -2 means: Rewrite the equation in slope-intercept form. y – 2x + 3 = STEP 2 Identify the slope and the y-intercept. = – 2 m and = 3 b STEP 3 Plot the point that corresponds to the y-intercept,(0, 3). STEP 4 Use the slope to locate a second point on the line. Draw a line through the two points.

Graph Using Slope and the Y-Intercept Graph the equation 3y – 2x = 3. Slope of 2/3 means: STEP 1 Rewrite the equation in slope-intercept form. y = + 1 2 3 x STEP 2 Identify the slope and the y-intercept. = 2/3 m and = 1 b STEP 3 Plot the point that corresponds to the y-intercept,(0, 1). STEP 4 Use the slope to locate a second point on the line. Draw a line through the two points.

Parallel Lines two lines in the same plane are parallel if they never intersect. Because slope gives the rate at which a line rises or falls, two lines with the SAME SLOPE are PARALLEL.

Line a and line c have the same slope, so they are parallel. Determine which of the lines are parallel. Find the slope of each line. – 1 – 0 – 1 – 2 = – 1 – 3 1 3 = Line a: m = – 3 – (–1 ) 0 – 5 – 2 – 5 = 2 5 = Line b: m = – 5 – (–3) – 2 – 4 – 2 – 6 = 1 3 = Line c: m = Line a and line c have the same slope, so they are parallel.