Write Equations of Lines

Slope Intercept Form: y = mx + b -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

Steps to Write the Equation of a Line in Slope-Intercept Form Use the equation y = mx + b Plug the slope into the m spot if it’s given (or calculate the slope from 2 points then plug in) Plug in the x and y values of one point (x,y) into the equation Solve that equation for b Plug the solution into the equation for the b value. Final equation will have x and y as variables and numbers as m and b

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 y=-2x+9 (plug in the m and b value into final equation)

Find the equation of a line with a slope of 4 and a point of (8, 3) on the line. 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= 4x - 29 (plug in the m and b value)

Find an equation for a line that passes through these points (1,6) and (3,-4) First find the slope of the line. Let x1, y1 be (1,6) and x2, y2 be (3,-4). M = y2 -y1 = -4 – 6 = -10 = x2-y1 3 – 1 2 -5

Now we know the m = -5 Pick either point 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: y = -5x + 11 Note - You can use either point in the equation and get the same answer.

Write an equation in slope-intercept form for the following points: (-3,2) and (5,-2). The slope of the line is: m = y2-y1 = -2-2 = -4 = -1 x2-x1 5-(-3) 8 2 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