Writing the Equation of a Line Given a Point and a Slope

Algebra Worksheet Writing Linear Equations

Writing the equation of a line given a point and a slope

Sample 1: Write the equation of the line with slope of 2 that goes through the point (-1,4).

Solution: We use the slope intercept form y= mx + b .

We know that the slope is 2 so our equation becomes y=2 x + b

From the point (-1, 4) we know that x=-1 and y =4 so we substitute them into the equation 4= 2( - 1) +b

Multiple 2(-1) to get the equation 4=- 2 +b

Now solve that equation by adding the opposite: 4= - 2 +b +2 + 2 6= b

The value of b is 6. The value of m is 2 (Slope is 2) so our answer is the equation y=2 x + 6

1: Write the equation for the line with slope of 2 through the point (6,-2). Show your work

Start with y= mx + b

Step 1: Write the equation with the slope of 2 in place of m:

Step 2: Substitute the values of x and y ( x=6, y=-2)

Step 3: Multiply and solve the equation for b

Now write your answer in the form of an equation

2. Write the equation for the line with slope of -4 through the point (1,3). Show your work

2 Sample 2: Write an equation for the line with slope of through the point (6,9) 3 2 Start: y= x + b Note: From the point (6,9) we know that x=6 and y =9 3 2 Substitute: 9= (6) +b 3

Multiply : 9= 4 +b Note: Use your calculator to multiply: (2� 3) 6 9= 4 +b Solve: -4 - 4 5= b

2 Write the answer: y= x +5 3

1 Practice: Write an equation with slope of through the point (5, 4) 2 Show your work: Follow the sample and write equations for the lines with the given slopes through the given points. Show your work:

1. m = 4, (3,1) 2. m = -1, (4,4)

2 1 3. m = , (6,8) 4. m = -, (10, - 2) 3 2

-1 5. m = -2.4, (0,1) 6. m = , (6,3) 3 Writing the equation of a line through two points

Sample 3: Write the equation of the line through (2,4) and (6, 6)

y- y Step 1. Find the slope. Use the formula m = 2 1 x2- x 1 6- 4 2 1 = = Note: write the fraction in simplest form. 6- 2 4 2

Step 2: Choose one of the points and use it to write the equation

1 1 Start: y= x + b Note: We found the slope was in step 1. 2 2

Choose a point: Choose (2,4) which means x=2 and y= 4 and substitute into the equation: 1 4= (2) + b 2 Multiply: 4= 1 + b Subtract 1 from each side -1 -1 3 = b 1 1 Write the equation: We know m = and b = 3 so the equation is y= x + 3 2 2

Does it matter which point we choose? What would happen if we had chosen the other point (6,6)? 1 Substitute x=6 and y=6 into the equation y= x + b 2 1 6= (6) + b 2 6= 3 + b Subtract 3 from both sides -3 -3 3 = b 1 The equation is y= x + 3 . It doesn’t matter which point we choose. We get the same 2 answer either way

骣 y- y Find the slope 琪m = 2 1 then write equation for the line between the following pairs of 桫 x2- x 1 points:

7. (2,4), (4,6) 8. (- 1,5), (7,3)

9. (3, 7) , (4, -1) 10. (6, 3), (3, 1)