Answer:
Point-slope:
y - 1 = -2(x - 4)
Slope-intercept:
y = -2x + 9
Standard:
2x + y = 9
Explanation:
The equation you were given is:
y = -2x + 7
This is slope-intercept form of the equation. When an eq is in this format you can see (no work!) the slope and the y-intercept (hence the name) Anyway, the number infrontof the x is the slope. Parallel lines have the same slope. So your new equation will also have a slope of -2.
We have a point on the new line, but not the y-intercept, so we need another form of the equation. Point-slope equation is something we can use.
y - y = m(x - x)
in this fill-in-the-blank formula, we put the slope in place of the m. And, given any point on the line (x,y) We fill in the SECOND x and the SECOND y. The FIRST x and y just stay variables.
So, we know the slope is -2.
And a point on the line is (4,1).
Fill in:
y - 1 = -2(x - 4)
This is the least- amount-of-work-for-us, equation of the line.
Sometimes the teacher/book/class/program asks for a specific version of the equation.
y - 1 = -2(x - 4)
Distribute the -2.
y - 1 = -2x + 8
Add 1 to both sides.
y = -2x + 9
This is slope-intercept form of the equation.
Or we can change it to Standard form.
y = -2x + 9
Add 2x to both sides.
2x + y = 9