Write the equation of a line in slope-intercept form that is parallel to y = 2x and goes through the point (1, 9).
the slope is 2, so
y-9 = 2(x-1)
now rearrange as needed
To find the equation of a line that is parallel to y = 2x and goes through the point (1, 9), we need to use the slope-intercept form of a line equation, which is y = mx + b.
Since the given line, y = 2x, is in slope-intercept form, we can see that the slope (m) of the line is 2.
Since a line that is parallel to y = 2x will have the same slope, we can conclude that the slope of the line we want to find is also 2.
Now, we can use the point (1, 9) and the slope (m = 2) to find the value of the y-intercept (b).
Using the point-slope form of a line equation, which is:
y - y1 = m(x - x1)
where (x1, y1) is the given point:
y - 9 = 2(x - 1)
Expanding the equation:
y - 9 = 2x - 2
Rearranging the equation to solve for y:
y = 2x - 2 + 9
Simplifying the equation:
y = 2x + 7
Therefore, the equation of a line in slope-intercept form that is parallel to y = 2x and goes through the point (1, 9) is y = 2x + 7.
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) of the line.
Given that we want a line that is parallel to y = 2x, we know that the parallel line will have the same slope. Therefore, the slope (m) of the line we want to find is also 2.
Next, we need to find the y-intercept (b). We can do this by substituting the coordinates of the point (1, 9) into the equation y = mx + b and solving for b.
Substituting the values:
9 = 2 * 1 + b
Simplifying:
9 = 2 + b
To isolate b, we subtract 2 from both sides:
9 - 2 = b
7 = b
Now that we have the slope (2) and the y-intercept (7), we can write the equation of the line in slope-intercept form (y = mx + b):
y = 2x + 7
Therefore, the equation of the line that is parallel to y = 2x and passes through the point (1, 9) is y = 2x + 7.