What is the equation of the line that goes through the points (4,3) and (8,2) ?
To find the equation of the line that goes through (4,3) and (8,2), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points and m is the slope of the line. We can find the slope using the slope formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the two given points. Substituting the values, we get:
m = (2 - 3)/(8 - 4) = -1/4
Now we can choose either of the given points and substitute into the point-slope form. Let's use (4,3):
y - 3 = (-1/4)(x - 4)
Expanding and simplifying, we get:
y = (-1/4)x + 7/2
This is the equation in slope-intercept form, where the slope is -1/4 and the y-intercept is 7/2.
To find the equation of the line that goes through the points (4,3) and (8,2), we can follow these steps:
Step 1: Determine the slope of the line using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Let the first point be (x1,y1) = (4,3)
Let the second point be (x2,y2) = (8,2)
Substituting the values into the formula:
m = (2 - 3) / (8 - 4)
m = -1 / 4
Step 2: Use the point-slope form of the equation, which is:
y - y1 = m(x - x1)
Substituting the point (x1,y1) = (4,3) and the slope m = -1/4:
y - 3 = (-1/4)(x - 4)
Step 3: Simplify the equation and write it in slope-intercept form (y = mx + b):
Distribute the -1/4 to the x - 4 expression:
y - 3 = (-1/4)x + 1
Add 3 to both sides of the equation to isolate y:
y = (-1/4)x + 4
Therefore, the equation of the line that goes through the points (4,3) and (8,2) is y = (-1/4)x + 4.