Question
slope form for (-3,3),(3,0)
Answers
GPT 3.5
To find the slope-intercept form of a linear equation using two given points, we can use the formula:
y - y₁ = m(x - x₁),
where (x₁, y₁) and (x, y) are two points on the line, and m is the slope of the line.
Given points: (-3, 3) and (3, 0)
First, let's find the slope, m:
m = (y₂ - y₁) / (x₂ - x₁)
m = (0 - 3) / (3 - (-3))
m = (-3) / 6
m = -1/2
Now, we can select one of the points, let's say (-3, 3), and substitute its coordinates along with the slope into the slope-intercept form:
y - y₁ = m(x - x₁)
y - 3 = (-1/2)(x - (-3))
y - 3 = (-1/2)(x + 3)
y - 3 = (-1/2)x - 3/2
To simplify, we can add 3 to both sides to isolate y:
y = (-1/2)x - 3/2 + 3
y = (-1/2)x - 3/2 + 6/2
y = (-1/2)x + 3/2
Therefore, the slope-intercept form of the line passing through the points (-3, 3) and (3, 0) is y = (-1/2)x + 3/2.
y - y₁ = m(x - x₁),
where (x₁, y₁) and (x, y) are two points on the line, and m is the slope of the line.
Given points: (-3, 3) and (3, 0)
First, let's find the slope, m:
m = (y₂ - y₁) / (x₂ - x₁)
m = (0 - 3) / (3 - (-3))
m = (-3) / 6
m = -1/2
Now, we can select one of the points, let's say (-3, 3), and substitute its coordinates along with the slope into the slope-intercept form:
y - y₁ = m(x - x₁)
y - 3 = (-1/2)(x - (-3))
y - 3 = (-1/2)(x + 3)
y - 3 = (-1/2)x - 3/2
To simplify, we can add 3 to both sides to isolate y:
y = (-1/2)x - 3/2 + 3
y = (-1/2)x - 3/2 + 6/2
y = (-1/2)x + 3/2
Therefore, the slope-intercept form of the line passing through the points (-3, 3) and (3, 0) is y = (-1/2)x + 3/2.