Write the equation of a line in slope intercept form that is parallel to the given line and passes through the given point.
y = 2x + 3
(1, 7)
is it
a) y = 2x + 9
b) y = 2x + 5
c) y = (1/2)x + 6.5
d) y = -(1/2)x + 7.5
To find the equation of a line that is parallel to the given line, we need to use the fact that parallel lines have the same slope. In the given equation, the slope is 2 (the coefficient of x).
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
Since the new line is parallel to the given line, the slope of the new line will also be 2.
To find the equation of the new line, we can now use the point-slope form of a line, which is
y - y1 = m(x - x1),
where (x1, y1) is the given point. Let's substitute the values:
y - 7 = 2(x - 1).
Now, we can simplify and rewrite the equation in slope-intercept form:
y - 7 = 2x - 2,
y = 2x - 2 + 7,
y = 2x + 5.
Therefore, the equation of the line that is parallel to y = 2x + 3 and passes through the point (1, 7) is y = 2x + 5.