Final answer:
To find an equation parallel to y=3x-2 and passes through (2,11), we need to find the slope of the given equation first. The equation we're looking for will also have a slope of 3. By plugging the values (x₁, y₁) = (2, 11) and m = 3 into the point-slope form, y - 11 = 3(x - 2), we can find the equation that is parallel to y=3x-2 and passes through (2,11).
Step-by-step explanation:
To find an equation that is parallel to y = 3x - 2 and passes through the point (2,11), we need to find the slope of the given equation. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The equation y = 3x - 2 has a slope of 3. Since parallel lines have the same slope, the equation we're looking for will also have a slope of 3.
Now, we can use the point-slope form of a linear equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope. Plugging the values (x₁, y₁) = (2, 11) and m = 3 into the point-slope form, we get:
y - 11 = 3(x - 2)
This is the equation that is parallel to y = 3x - 2 and passes through the point (2,11).