Write Equations of Lines Slope Intercept Form of

Slope Intercept Form of a Linear Function: f(x)=ax+b y=mx+b You will be able to:

Steps to Write the Equation of a Line in Slope-Intercept Form Use the linear

Write an equation of the line that passes through the point (6, -3) with

Find an equation for a line that passes through these points (1, 6) and

Now we know the m = -5 Pick either point. Let’s use (1, 6)

Write the Equation from the Table First find the slope m = y 2

Write the Equation from the Graph • Find (-3, 2) the slope of the

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Write Equations of Lines

Slope Intercept Form of a Linear Function: f(x)=ax+b y=mx+b You will be able to: -Find the equation of a line when you are given the slope of the line and any point on the line. -Find the equation of a line when you are only given two points on the line -Write equations from ordered pairs, tables, and graphs

Steps to Write the Equation of a Line in Slope-Intercept Form Use the linear function f(x)=ax+b equation y = mx + b 1. Plug the slope into the m it may be given or you may need to calculate the slope 2. Plug in the x and y values of one point (x, y) into the equation 3. Solve that equation for b 4. Plug the b solution and slope into equation Final equation will have x and y as variables and numbers as m and b. ie. y=2 x-6 or y=-1/3 x+9

Write an equation of the line that passes through the point (6, -3) with a slope of -2. Follow the steps: y = mx + b -3 = -2(6) + b (plug in given m, x, and y) -3 = -12 + b (solve for b, add 12 to both sides) 9=b (plug in the m and b value into final equation) y=-2 x+9

Find an equation for a line that passes through these points (1, 6) and (3, -4) • First find the slope of the line. • Let • M x 1, y 1 be (1, 6) and x 2, y 2 be (3, -4). = y 2 -y 1 = -4 – 6 = -10 = x 2 -y 1 3– 1 2 -5

Now we know the m = -5 Pick either point. Let’s use (1, 6) so x = 1, and y = 6. Next solve for b. Substitute into y= mx + b. • 6= (-5)(1) + b • 6= -5 +b • 11=b The y- intercept is b=11. • So the final equation is: • Note y = -5 x + 11 - You can use either point in the equation and get the same answer.

Write the Equation from the Table First find the slope m = y 2 -y 1 = -5 – -13 = 8 = x 2 -y 1 6– 4 2 slope of 4 Then select a point to use (8, 3) I picked this one because the x and y are both small positive values – easy to work with! Follow the steps: y = mx + b 3 = 4(8) + b (plug in m, x, and y) 3 = 32 + b (solve for b, subtract 32 from both sides) -29 = b y= 4 x - 29 (plug in the m and b value) x 4 6 8 10 y -13 -5 3 11

Write the Equation from the Graph • Find (-3, 2) the slope of the line: m = y 2 -y 1 = -2 -2 = -4 = (5, -2) x 2 -x 1 5 -(-3) 8 • To find the y- intercept, substitute the slope for -½ and use (-3, 2 ) for (x, y) in the slope-intercept form. 2= (-1/2)(-3) + b 2= 3/2 + b ½= b • Equation y= -½x + ½ -½