To find a point that satisfies both equations, we need to find their point of intersection.
A
a
x=-9, see solution.
B
b
y=0.5x+6.5
C
c
(1.4,5.8)
Practice makes perfect
a
In order to find the value of x, we first have to find the slope of the line 2x+y=3. This will allow us to find the slope of a line perpendicular to the given one. The given equation is in the standard form, so we will rearrange it so that it is written in slope-intercept form first.
In this equation the coefficient of the x variable gives the slope of the line, -2. Perpendicular lines have negative reciprocals for their slopes. In this case, this will be 12. Since we can calculate the slope using the two given points on the line, ( -1, 6) and ( x, 2), we can use the Slope Formula to solve for the missing x value.
Now, having the slope and a point on the line, we can write a new equation using the point-slope form. We have found that the slope is 12, or 0.5, and we can use the point (-1,6), so m= 0.5 and ( x_1, y_1)=( -1, 6).
The equation of the line perpendicular to the given line 2x+y=3 and through the given points is y=0.5x+6.5.
c
To find a point that is a solution to both equations, we need to find their point of intersection. One way to do this is by equating the lines and solving for x.
