Write an equation in standard form of the line that passes through the given points
(-1,2) (5,4)
I not sure about this one can someone show me how to do it?
slope = (4-2)/(5-(-1)) = 1/3
pick (5,4)
y-4 = (1/3)(x-5)
times 3
3y - 12 = x - 5
x - 3y = -7
check: does the point I didn't use satisfy the equation?
for (-1,2)
LS = -1 - 3(2)
= -7
= RS
......... all is good!
Thank You
To find the equation of a line in standard form, you can use the formula:
Ax + By = C
where A, B, and C are constants.
Step 1: Find the slope of the line
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-1, 2) and (5, 4), the slope would be:
m = (4 - 2) / (5 - (-1))
= 2 / 6
= 1/3
Step 2: Use the slope-intercept form to find the equation
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the slope (1/3) and one of the given points (5, 4) into the equation, we can solve for b:
4 = (1/3)(5) + b
4 = 5/3 + b
12/3 - 5/3 = b
7/3 = b
So the equation in slope-intercept form is:
y = (1/3)x + 7/3
Step 3: Convert to standard form
To convert the equation to standard form (Ax + By = C), we multiply the entire equation by 3 to eliminate any fractions:
3y = x + 7
Then we rearrange the equation to have x and y terms on the same side:
x - 3y = -7
So, the equation of the line passing through the points (-1, 2) and (5, 4) in standard form is:
x - 3y = -7