Find the equation of a line that passes through the points (4, 3) and (8, 1).
1.Find Slope
m=
2. Pick a point
3. Plug in AND solve for b
y=mx+b
b=
4. Write the equation using m and b from step 1 and 2
1. Find Slope:
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4, 3) and (8, 1), we can substitute the coordinates into the formula to find the slope:
m = (1 - 3) / (8 - 4)
m = -2 / 4
m = -1/2
2. Pick a point:
Let's choose the point (4, 3) as our point to plug into the equation.
3. Plug in AND solve for b:
Using the point-slope form of a linear equation (y - y1) = m(x - x1), we can substitute the values:
(y - 3) = (-1/2)(x - 4)
To find the value of b, we can solve for y by expanding the equation:
y - 3 = (-1/2)(x - 4)
y - 3 = (-1/2)x + 2
Now, we isolate y by moving -3 to the right side of the equation:
y = (-1/2)x + 2 + 3
y = (-1/2)x + 5
Therefore, b = 5.
4. Write the equation using m and b from steps 1 and 3:
The equation of the line that passes through the points (4, 3) and (8, 1) is:
y = (-1/2)x + 5