Find the equation of the line (in y = mx + c form) that:
has gradient 2, passing through the intersection of the lines with equations y= 3x - 5 and y= -2x + 5.
Show any working out...thanks!
To find where the lines intersect, solve the system of equations that they represent.
Since they're already both solved for "y=", I'd use substitution. So set it up like so:
. . . . .$\displaystyle 3x\, -\, 5\, =\, -2x\, +\, 5$
. . . . .$\displaystyle 3x\, +\, 2x\, =\, 5\, +\, 5$
...and so forth. This will give you the point $\displaystyle (x_1,\, y_1)$ of intersection.
You are already given the slope (or gradient): $\displaystyle m\, =\, 2$. Plug this information into whichever straight-line equation you prefer. Since you have a point and a slope, you might want to start with the point-slope form:
. . . . .$\displaystyle y\, -\, y_1\, =\, m(x\, -\, x_1)$
Multiply the slope through the parentheses, and then solve for "y=". The result is the equation you need.
If you get stuck, please reply showing how far you have gotten in working through the steps. Thank you!
3x - 5 = -2x + 5 y = -2(2) + 5
5x = 10 = -4 + 5
x = 2 = 1
y - 1 = 2(x - 2)
y - 1 = 2x - 4
y = 2x - 3
Thanks! Earlier I tried this method but I made a rearragement error.
i.e at the start I went:
3x - 5 = -2x + 5
5x - 25 = 0
instead what's in the above. Happens when I'm tired!