To start, the equation has to be converted to slope-intercept form, or . Start by subtracting x from both sides;
,
. Switch 4 and -x around to conform to the formula;
. Then divide by 2 to isolate y;
. This is the final equation. Because the slope of a line perpendicular is always the opposite reciprocal (i.e. The opposite reciprocal of 4 is
, the opposite reciprocal of
is 5) the opposite reciprocal of
is 2. So the equation of the line is
, and the answer is A.
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
second equation:
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
