What is an equation of the line that passes through the points left bracket, 2, comma, 2, right bracket
(
2
,
2
)
(2,2) and left bracket, 1, comma, minus, 2, right bracket
(
1
,
−
2
)
(1,−2)?
To find the equation of the line passing through two points, we need to find the slope (m) and the y-intercept (b).
Given the points (2, 2) and (1, -2):
1. Find the slope:
m = (y₂ - y₁) / (x₂ - x₁)
m = (-2 - 2) / (1 - 2)
m = -4 / -1
m = 4
2. Use the slope-intercept form of a linear equation (y = mx + b) to find the y-intercept:
Choose one of the points, let's use (2, 2):
2 = 4(2) + b
2 = 8 + b
b = -6
3. Substitute the slope (m) and y-intercept (b) into the equation:
y = 4x - 6
Therefore, the equation of the line that passes through the points (2, 2) and (1, -2) is y = 4x - 6.
To find the equation of a line passing through two points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one point on the line and m is the slope of the line.
Given the points (2, 2) and (1, -2), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-2 - 2) / (1 - 2)
m = (-4) / (-1)
m = 4
Now, using the first point (2, 2), we can plug the values into the point-slope equation:
y - y1 = m(x - x1)
y - 2 = 4(x - 2)
y - 2 = 4x - 8
y = 4x - 8 + 2
y = 4x - 6
Therefore, the equation of the line passing through the points (2, 2) and (1, -2) is y = 4x - 6.