5 1 WRITING LINEAR EQUATIONS IN SLOPEINTERCEPT FORM

5. 1 WRITING LINEAR EQUATIONS IN SLOPEINTERCEPT FORM 5. 2 WRITING LINEAR EQUATIONS GIVEN THE SLOPE AND A POINT

QUICK REVIEW An equation of a line can be written in slopeintercept form y = mx + b where m is the slope and b is the y-intercept. The y-intercept is where a line crosses the yaxis.

WRITING AN EQUATION OF A LINE Suppose the slope of a line is 5 and the yintercept is 2. How would this you write the equation of this line in slope-intercept form? First write the slope-intercept form. y = mx + b Now substitute 5 for m and 2 for b. y = 5 x + 2

WRITE THE EQUATION OF A LINE FROM A GRAPH y = mx + b y = 2 x + (-4) y = 2 x -4 Where does the line cross the y-axis? ◦ At the point (0, -4) ◦ The y-intercept is -4. What is the slope of the line? ◦ The graph also crosses the x-axis at (2, 0). ◦ We can use the slope formula to find our slope. m = -4 – 0 = -4 = 2 0 – 2 -2 We know our slope is 2 and our y-intercept is -4, what is the equation of our line?

LET’S TRY SOME EXAMPLES! Write the equation of a line with a slope of -2 and a yintercept of 6. y = mx + b y = -2 x + 6 Write the equation of a line with a slope of -4/3 and a y-intercept of 1. y = mx + b y = (-4/3) + 1

USING A GRAPH Where does the line cross the y-axis? At the point (0, 2) ◦ So the y-intercept b is 2. ◦ The line also passes through the point (3, 0). We can use these points to find the slope of the line. How? What formula do we use? Using the slope formula, we find that the slope m is 2/3. ◦ Write the equation of the line. ◦ y= mx + b y = (-2/3)x + 2

EXAMPLE 1 b = -3 m= +2 y= x-3 +3 y x

EXAMPLE 2 b=1 m= y= -2 +1 x+1 y x

FIND THE EQUATION OF A LINE GIVEN THE GRAPH • • • Find the y-intercept from the graph. Count the slope from the graph. To write the equation of the line, substitute the slope and y-intercept in the slope-intercept form of the equation.

Write it in slope-intercept form. (y = mx + b) 5 x – 3 y = 6 -3 y = -5 x + 6 -3 -3 -3 y= x-2 m= b = -2

Write it in slope-intercept form. (y = mx + b) 2 y + 2 = 4 x 2 y = 4 x - 2 2 y = 2 x - 1 m=2 b = -1

IF WE ARE GIVEN THE SLOPE AND A POINT Step 1: First find the y-intercept. Substitute the slope m and the coordinates of the given point (x, y) into the slope-intercept form, y = mx + b. Then solve for the y-intercept b. Step 2: Then write the equation of the line. Substitute the slope m and the y-intercept b into the slopeintercept form, y = mx + b.

IF WE ARE GIVEN THE SLOPE AND A POINT Suppose we have a slope of -3 and it passes through the point (1, 2). ◦ We first need to find the y-intercept. We can do this by substituting our information into slope -intercept form and solving for b. y = mx + b 2 = -3(1) + b 2 = -3 + b 5 = b is 5. y = mx + b y = -3 x + 5 Add 3 to both sides. Now we know that the y-intercept

TRY THESE! Suppose we have a line with a slope of -1 and passes through the point (3, 4). y = mx + b 4 = (-1)3 + b 4 = -3 + b 7=b y = mx + b y = (-1)x + 7 y = -x + 7 Suppose we have a line with a slope of 2 and passes through the point (1, 3). y = mx + b 3 = 2(1) + b 3=2+b 1=b y = mx + b y = 2 x + 1

Write an equation of the line that goes through the points (-2, 1) and (4, 2). To write an equation, you need two things: slope (m) and y – intercept (b) We need both!! First, we have to find the slope. Plug the points into the slope formula. Simplify

Write an equation of the line that goes through the points (-2, 1) and (4, 2). slope (m) = y – intercept (b) = ? ? ? Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use? (4, 2) because both numbers are positive. 2 = (4) + b

Writing Equations given two points 2= Solve the equation for b 2= (4) + b +b To write an equation, you need two things: slope (m) = y – intercept (b) =

WRITING EQUATIONS OF PARALLEL LINES Two nonvertical lines are parallel if and only if they have the same slope. Write the equation of a line that is parallel to the line y = 4 x -3 and passes through the point (3, 2). Since the two lines are parallel then both lines have a slope of m = 4. ◦ We must substitute the slope and coordinates into the slope-intercept form and solve for b. ◦ ◦ 2 = 4(3) + b 2 = 12 + b -10 = b Subtract 12 from both sides Now we have enough information to write the equation of the line. y = mx + b y = 4 x + (-10) y = 4 x -10

ALMOST DONE! Write the equation of a line that is parallel to the line y = -2 x -3 and passes through the point ( -2, 3). Since they are parallel, they both have the same slope m of -2. ◦ Now substitute our slope and coordinates into slope -intercept form. ◦ Write the equation of a line that is parallel to the line y = 3 x + 2 and passes through the point (4, -1). Since they are parallel, they both have the same slope m of 3. ◦ Now substitute our slope and coordinates into slope -intercept form. ◦ 3 = -2(-2) + b 3 = 4 + b -1 = b ◦ Now we can write the equation of the second line. y = mx + b y = -2 x -1 = 3(4) + b -1 = 12 + b -13 = b ◦ Now we can write the equation of the second line. y = mx + b y = 3 x -13