Essential Question: How do you graph and write linear equations using point-slope form? 5.4 Point-Slope Form

5.2 Slope-Intercept Form Review What is slope-intercept form?What is slope-intercept form? What does m represent?What does m represent? What does slope tell us about a line?What does slope tell us about a line? What does b represent?What does b represent? What does the y-intercept tell us about a line?What does the y-intercept tell us about a line? What is slope-intercept form useful for?What is slope-intercept form useful for?

5.3 Standard Form Review What is standard form?What is standard form? What do A, B, and C represent?What do A, B, and C represent? What is standard form useful for?What is standard form useful for?

Use Slope & a Point to Graph If you have the slope and a point of a linear equation, do you have enough information to graph? Slope= 3 Point= (1,1)

Use Slope & a Point to Graph 1)Slope = -1/2 Point = (3, -2)

POINT-SLOPE FORM Point-Slope formPoint-Slope form –The line with slope m that contains the point (x 1, y 1 ) can be described by the equation y – y 1 = m(x –x 1 ) –USES: Good when you have the slope and a regular point (no intercept), and you want to write an equation or graph Easy to simplify point-slope form into slope-intercept form Good when you have two points, and you need to write an equation or graph

Write an Equation In Point-Slope Form To write an equation in point-slope formTo write an equation in point-slope form –Substitute the slope for m –Substitute for (x 1, y 1 ) –Simplify

WRITE AN EQUATION IN POINT-SLOPE FORM FOR THE LINE WITH THE GIVEN SLOPE THAT CONTAINS THE GIVEN POINT. 1) SLOPE = 2, (1/2, 1)2) SLOPE = 0, (3, -4) Practice

Point-Slope Form to Slope-Intercept Form Point-slope form can be simplified to slope-intercept form, so this is a useful skill.Point-slope form can be simplified to slope-intercept form, so this is a useful skill. –1) Substitute –2) Distribute –3) Inverse operation EXAMPLE 2:EXAMPLE 2: m = 1/3, (-3, 1)m = 1/3, (-3, 1)

Simplify to Slope-Intercept Form Point-Slope Form to Slope-Intercept Form: 1)Distribute the slope value 2)Inverse operation to isolate the y-value

WRITE AN EQUATION IN SLOPE-INTERCEPT FORM FOR THE LINE BY USING POINT-SLOPE FORM TO SIMPLIFY. 1) SLOPE = 3, (-1,4) 2) M= 0, (0,2) Practice

Two Points to Write an Equation If you were given two points, and you needed to write a linear equation, what would you do?If you were given two points, and you needed to write a linear equation, what would you do? –1) Use the slope formula to find m –2) Substitute –3) Distribute –4) Inverse (1,-4) and (3,2)

WRITE AN EQUATION IN SLOPE-INTERCEPT FORM. 1) (1, -2) & (3,10) 2) (6,3) & (0, -1) PRACTICE

WORD PROBLEMS

FORMS REVIEW FORMS OF LINEAR EQUATIONS STANDARD FORM Ax + By = C 2x + 3y = 5 Uses: Identify x & y intercepts Identify A,B, & C SLOPE-INTERCEPT FORM y= mx + b y = -2/3x + 5 Uses: If you have the m & b, 1) Writing an equation 2) Graphing POINT-SLOPE FORM y – y1 = m(x – x1) y – 7 = 3(x - 4) Uses: If you have m and a point, 1) Writing an equation 2) Graphing 3) Simplifying to slope-intercept form Uses: If you have two points 1) Writing an equation 2) Graphing

1)WHAT IS POINT-SLOPE FORM? 2)WHAT IS POINT-SLOPE FORM USEFUL FOR? 3)HOW DO YOU SWITCH FROM POINT-SLOPE FORM TO SLOPE-INTERCEPT FORM? 4)GIVEN TWO POINTS, WHAT ARE THE STEPS IN WRITING AN EQUATION OF THE LINE THROUGH THOSE POINTS? 5.6 REVIEW

Summary Answer the essential questions in detailed, complete sentences. How do you graph and write linear equations using point-slope form? Write 2-4 study questions in the left column to correspond to the notes.