Write the equation of the line parallel to the line y+2x+3 containing the point (2,6). Slope intercept form.
Is that y = 2x+3 or y+2x+3 = 0?
I'll demonstrate with y = 2x+3. If that's wrong, then you can fix it and follow the same steps
we have a slope=2 and a point (2,6)
y-6 = 2(x-2) -- point-slope form
y = 2x + 2 -- slope-intercept form
Thank you very much Steve.
To find an equation of the line parallel to the given line and passing through the point (2,6), we need to determine the slope of the given line.
The given equation is in the standard form of a line, which is Ax + By = C. To write it in slope-intercept form (y = mx + b), we need to isolate y.
The equation y + 2x + 3 = 0 can be rewritten as y = -2x - 3. Now we can see that the slope of this line is -2.
Since we want to find a line parallel to this, the parallel line will have the same slope of -2.
Using the point-slope form of a linear equation (y - y₁ = m(x - x₁)), we can substitute the slope (-2) and the coordinates of the given point (2,6) into the equation:
y - 6 = -2(x - 2)
Now, let's simplify the equation:
y - 6 = -2x + 4
y = -2x + 10
So, the equation of the line parallel to y + 2x + 3 and passing through the point (2,6) in slope-intercept form is y = -2x + 10.