Part 1: When writing linear equations, how do you determine which form of a line to use?
Part 2: Choose 1 set of points from the choices below. Then, solve the problem and post your solution, showing your steps.
Write an equation in point-slope form for the line that passes through one of the following pairs of points (you may choose the pair you want to work with). Then, use the same set of points to write the equation in standard form and again in slope-intercept form.
Point pairs
(5, 1), (–3, 4)
(0, –2), (3, 2)
(–2, –1), (1, 2)
Part 3: View and comment on the work of at least 2 other students. If possible, choose students' whose work is based on different sets of points from the ones you chose.
I need help from Steve and or Reiny, I've done work similar to this but not this.....
Different texts use slightly different names for the form of the linear equation.
e.g
4x + 3y -12 = 0 -----> I would call general form
4x + 3y = 12 -------> standard form
y = (-4/3)x + 4 ---- > slope-y intercept form
point-slope form is a starting equation, usually ending up with one of the above.
Which ever method you use, finding the slope is a good start.
I will do the first one:
2 points (5,1) and (-3,4)
slope = (4-1)/(-3-5) = 3/-8 or -3/8
using (5,1)
y-1 = (-3/8)(x-5) from y - y1 = m(x - x1)
at this point multiply each side by the denominator of the slope, if the slope is a fraction
8y - 8 = -3(x-5)
your fractions have disappeared, yeahhh!
8y - 8 = -3x + 15
3x + 8y = 23
at this stage I use the point that was not used and test if it satisfies my equation.
for (-3,4)
LS = 3(-3) + 8(4) = -9+32 = 23
RS = 23 , all is good!
Once you have the equation is the simple form of
3x + 8y = 23, you can go to any of the others
changing it to slope - y intercept form takes 2 steps
1. keep only the y term on the left side
3x + 8y = 23 -------> 8y = -3x + 23
2. divide each term by the coeffiecient of the y term
------> y = (-3/8)x) + 23/8
try the other two, let me know what you get
Part 2:
The point pairs chosen is (5, 1) and (-3, 4). First of all, the slope must be found out.
The formula for it is: slope = rise/run
slope = (4 - 1)/(-3 -5) = 3/-8 = -3/8
Point slope form: y - 1 = -3 (x - 5)/8
Slope intercept form: y - 1 = -3x/8 + 15/8
y = -3x/8 + 23/8
Standard form: 8y = -3x + 23
Thats all I rlly needed, thx~!
Part 1: When writing linear equations, there are three common forms you can use:
1. Slope-intercept form: y = mx + b
This form is useful when you know the slope (m) and the y-intercept (b) of the line.
2. Point-slope form: y - y1 = m(x - x1)
This form is useful when you know the slope (m) and the coordinates of a point on the line (x1, y1).
3. Standard form: Ax + By = C
This form is useful when you need to express the equation in a more general form, where A, B, and C can be any real numbers.
To determine which form to use, you need to consider the given information.
- If you have the slope and y-intercept, you can directly use the slope-intercept form.
- If you have the slope and a point, you can use the point-slope form.
- If you have two points, you can calculate the slope using the formula (y2 - y1) / (x2 - x1), and then plug in the slope and one of the points into the point-slope form or use the standard form.
Part 2: Let's choose the first pair of points: (5, 1) and (-3, 4).
To write the equation in point-slope form:
1. Calculate the slope using the formula: m = (y2 - y1) / (x2 - x1).
So, m = (4 - 1) / (-3 - 5) = 3 / -8.
2. Choose one of the points (let's use (5, 1)) and substitute the values into the point-slope form: y - y1 = m(x - x1).
We get, y - 1 = (3 / -8)(x - 5).
To write the equation in standard form:
1. Distribute the slope: y - 1 = (3 / -8)x + (15 / 8).
Multiplying everything by 8 to eliminate the fraction, we get 8y - 8 = -3x + 15.
2. Rearrange the equation in standard form: 3x + 8y = 23.
To write the equation in slope-intercept form:
1. Solve the point-slope form equation for y.
We get, y = (3 / -8)x + (8 / 8) + (1 / 8), which simplifies to y = (3 / -8)x + (9 / 8).
Part 3: Since I'm an AI, I cannot directly access the work of other students. It would be best for you to review the work of two other students and provide your comments based on their solutions. Remember to consider the differences in the point pairs chosen and any errors or inaccuracies in their work.