For #1-4, write an equation of the line that passes through each pair of points. Show all of your work to receive full credits.
1.) (9, -2) and (4, 3)
Answer: 9 = -1x + -2
2.) (3, 5) and (2, -2)
Answer: 3 = 7x + 5
3.) (4, 3) and (2, 0)
Answer: 4 = 2/3x + 3
4.) (5, 2) and (15, -10)
Answer: 15 = -6/5x + -10
Could someone please check my work? Thanks so much :)
none are correct
A typical equation of a straight line, other than vertical or horizontal lines, need an x and a y variable.
I will do one of them , say #4, you do the others
slope of line = (-10-2)/(15-5) = -12/10 = -6/5
using the point (5,2),
y - 2 = (-6/5)(x-5)
multiply both sides by 5
5y - 10 = -6x + 30
6x + 5y = 40
or in the form y = mx + b
y = (-6/5)x + b
sub in the point (5,2)
2 = (-6/5)(5) + b
2 = -6 + b
b = 8
y = (-6/5)x + 8
use whichever method you learned.
Thanks so much! My teacher explained it really terribly and I didn't realize until I turned in the homework assignment I missed entire steps :P
To find the equation of a line that passes through two points, you can use the point-slope formula:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
1.) (9, -2) and (4, 3)
To find the slope (m), use the formula:
m = (y2 - y1) / (x2 - x1)
m = (3 - (-2)) / (4 - 9)
m = 5 / -5
m = -1
Choose one of the points, let's say (9, -2), and substitute the values into the point-slope formula:
y - y1 = m(x - x1)
y - (-2) = -1(x - 9)
y + 2 = -x + 9
y = -x + 9 - 2
y = -x + 7
So, the equation of the line in slope-intercept form is y = -x + 7.
2.) (3, 5) and (2, -2)
Using the same process, we find:
m = (-2 - 5) / (2 - 3)
m = -7 / -1
m = 7
Substituting the values of (3, 5) into the point-slope formula:
y - y1 = m(x - x1)
y - 5 = 7(x - 3)
y - 5 = 7x - 21
y = 7x - 21 + 5
y = 7x - 16
So, the equation of the line is y = 7x - 16.
3.) (4, 3) and (2, 0)
Using the same process:
m = (0 - 3) / (2 - 4)
m = -3 / -2
m = 3/2
Substituting (4, 3) into the point-slope formula:
y - y1 = m(x - x1)
y - 3 = (3/2)(x - 4)
y - 3 = (3/2)x - 6
y = (3/2)x - 6 + 3
y = (3/2)x - 3
So, the equation of the line is y = (3/2)x - 3.
4.) (5, 2) and (15, -10)
Following the same steps:
m = (-10 - 2) / (15 - 5)
m = -12 / 10
m = -6/5
Using (5, 2) in the point-slope formula:
y - y1 = m(x - x1)
y - 2 = (-6/5)(x - 5)
y - 2 = (-6/5)x + 6
y = (-6/5)x + 6 + 2
y = (-6/5)x + 8
So, the equation of the line is y = (-6/5)x + 8.
Please double-check your work with these solutions.