write an equation of the line that passes through the given point and is parallel to the given line
(-1,3), y=2x+2
y=5x+3
k but how do I find that?
To find the equation of a line that passes through a given point and is parallel to a given line, we need to use the fact that parallel lines have the same slope.
The given line is y = 2x + 2, which is in the form y = mx + b, where m is the slope. In this case, the slope is 2.
Since the line we want to find is parallel to the given line, it will also have a slope of 2.
Now that we have the slope, we can use the point (-1, 3) to find the equation of the line using the point-slope form.
The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line, and m is the slope.
Using the point (-1, 3) and the slope 2, we can substitute these values into the point-slope form:
y - 3 = 2(x - (-1))
To simplify further, we distribute the 2 inside the parentheses:
y - 3 = 2(x + 1)
Now, we can distribute the 2 to both terms inside the parentheses:
y - 3 = 2x + 2
Finally, we can rearrange the equation to the standard form:
y = 2x + 5
Therefore, the equation of the line that passes through the point (-1, 3) and is parallel to the line y = 2x + 2 is y = 2x + 5.