write an equation of the line that passes through (2, -1) and (-3,3).
what is the slope?
m = (3 - -1) / (-3 -2) = 4/-5 = -4/5
so
y = - 4 x/5 + b
put a point in
-1 = -8/5 + b
b = 8/5 - 5/5 = 3/5
so
y = -4x/5 +3/5
5 y = -4 x + 3
the slope is (3+1)/(3-2) = 4
Now you have a point and a slope, so use the point-slope form of the line:
y+1 = 4(x-2)
Thank you!
Oops. Pesky minus sign!
write an equation of the line that passes through (2, -1) and (-3,3).
write an equation of the line that passes through (2, -1) and (-3,3).
Sure! Let me use my clown magic to come up with a hilarious equation for you.
Let's first find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points, we have:
m = (3 - (-1)) / (-3 - 2)
m = 4 / -5
m = -4/5
Now, let's find the equation using the point-slope form:
y - y1 = m(x - x1)
Substituting one of the points, let's say (2, -1), we get:
y - (-1) = (-4/5)(x - 2)
y + 1 = (-4/5)(x - 2)
And voila! We have a funny equation for the line:
y + 1 = (-4/5)(x - 2)
Feel free to laugh at this equation while plotting the line!
To find the equation of a line, we can use the slope-intercept form of the equation, which is given by:
y = mx + b
Where:
m is the slope of the line
b is the y-intercept
To find the slope (m) of the line passing through the points (2, -1) and (-3, 3), we can use the formula:
m = (change in y) / (change in x)
Let's calculate the slope:
change in y = -1 - 3 = -4
change in x = 2 - (-3) = 2 + 3 = 5
So, the slope (m) = -4/5.
Now that we have the slope (m), we can find the y-intercept (b) using one of the given points. Let's use the point (2, -1):
y = mx + b
-1 = (-4/5)(2) + b
Simplifying the equation:
-1 = -8/5 + b
To find b, we can rearrange the equation:
b = -1 + 8/5
b = -5/5 + 8/5
b = 3/5
So, the y-intercept (b) is 3/5.
Now, we have the slope (m = -4/5) and the y-intercept (b = 3/5). Plugging these values into the slope-intercept form of the equation, we get:
y = (-4/5)x + 3/5
Therefore, the equation of the line passing through (2, -1) and (-3, 3) is y = (-4/5)x + 3/5.