Algebra 2- General Equation of a Line

5/3

Find the slope of the line whose equation is 0.05x - 0.03y = 9. 5/3 3/5 -5/3

3/2

Find the slope of the line whose equation is 15 + 3x = 2y. 3/2 -3/2 15/2

7/3

Find the slope of the line whose equation is 17 + 3y = 7x. 17/3 -7/3 7/3

-17/12

Find the slope of the line whose equation is 17x - 12y = -36. -17/12 17/12 -12/17

5

Find the value of the y-intercept of the line whose equation is 10x + 9y = 45. 9/2 2/9 5

-4

Find the value of the y-intercept of the line whose equation is 20x - 22y = 88. 4 10/11 -4

2

Find the value of the y-intercept of the line whose equation is 2x + 3y = 6. 2 3 6

Okay, the first thing to do here is calculate something known as the "slope". The slope is represented by "m" in the standard form: y = mx+b The slope is also known as the rise over the run, y2-y1/x2-x1 Substitute those points in: (-8,0) and (1,5) ==== 5-0/1-(-8) = 5/9 The slope is 5/9 Now we have to use the slope, and resubstitute another point to get y-intercept (1,5) 5 = 5/9(1)+b 5-5/9 =b b=4.444 Therefore, the standard equation of the line is {{ y =5/9x+4.4445

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (6, 1) and (5, 4)

The equation of a line in "standard form" is Ax + By + C = 0. First, find the slope of the line connecting (7, -3) and (4, -8): -8-[-3] -5 m = ------------- = ------- = 5/3 4-7 -3 Now use the point-slope form y-k = m(x-h) to come up with a first equation: y - [-3] = (5/3) (x-7), or y+3 = (5/3)x - 35/3 Multiply this through by 3 to eliminate the fraction 35/3: 3y + 9 = 5x - 35 Now rewrite this in "std. form:" 5x - 3y -35 - 9 = 0, or 5x - 3y - 44 = 0 This is the equation of the line in standard form. Note that (4, -8) satisfies this equation: 5(4) - 3(-8) - 44 = 0 20 + 24 - 44 = 0 is true.

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (7, -3) and (4, -8)

-2x+y=2

Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

-2x+y=-4

Write the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y = -5. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

The answer is â€"x + y = 0; An equation of a parallel line will have the same slope and also have a y intercept of 0. First, rewrite the equation in “y=mx+b” form to easily see the slope, m: y = -1x + 6 Our slope is -1, therefore, the parallel line through the origin would have an equation of y = -1x + 0, which is equivalent to y = -x. Rearrange the equation into standard form to get the final answer: -x + y = 0

Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

4

Find the value of the y-intercept of the line whose equation is 5x + 6y = 24 24/5 4 -4

4

Find the value of the y-intercept of the line whose equation is 5x - 3y = -12. 4 -12/5 -4

- It will be horizontal.

In the general equation of a line, if m = 0, what will the graph of the line look like? - It will be vertical. - It will be horizontal. - It will be equivalent to the graph of y = x. - There is not enough information to tell.

Okay, the first thing to do here is calculate something known as the "slope". The slope is represented by "m" in the standard form: y = mx+b The slope is also known as the rise over the run, y2-y1/x2-x1 Substitute those points in: (-8,0) and (1,5) ==== 5-0/1-(-8) = 5/9 The slope is 5/9 Now we have to use the slope, and resubstitute another point to get y-intercept (1,5) 5 = 5/9(1)+b 5-5/9 =b b=4.444 Therefore, the standard equation of the line is {{ y =5/9x+4.4445

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (-8, 0) and (1, 5)