A line passes through the point (0,3) and is parallel to the line 4x−5y=10. Find its intersection point with the line y=−2x+7.

Step-by-step solution

1. Rearrange $4x-5y=10$ to slope–intercept form: $y=(4/5)x-2$, giving slope $m=4/5$.
2. Since the required line is parallel, it also has slope $4/5$ and passes through $(0,3)$.
3. Write its equation: $y=(4/5)x+3$.
4. Set this equal to $y$ from the second line: $(4/5)x+3=-2x+7$.
5. Solve for $x$: $(4/5+2)x=4\Rightarrow (14/5)x=4\Rightarrow x=20/14=10/7$.
6. Substitute $x=10/7$ into $y=-2x+7$: $y=-2(10/7)+7=-20/7+49/7=29/7$.
7. Therefore the intersection point is $(10/7,29/7)$.

Concept tested: Parallel lines & intersection

Published 16 October 2026 · How this solution was prepared and checked