Final answer:
To write the equation of a line that passes through two given points in slope-intercept form, calculate the slope using the formula (y₂ - y₁) / (x₂ - x₁), then substitute the coordinates of one point and the slope into the equation y - y₁ = m(x - x₁).
Step-by-step explanation:
To write the equation of a line that passes through two given points (-1, 2) and (6, 3) in slope-intercept form, we can use the formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) represent the coordinates of one point, m represents the slope, and (x, y) represent the general coordinates of any other point on the line.
First, we can calculate the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging the values into the formula, we get:
m = (3 - 2) / (6 - (-1)) = 1/7
Next, we can choose one of the given points, let's say (-1, 2), and substitute its coordinates (x₁, y₁) into the formula:
y - 2 = (1/7)(x - (-1))
Simplifying, we get:
y - 2 = (1/7)(x + 1)
This is the equation of the line passing through the points (-1, 2) and (6, 3) in slope-intercept form.
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