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 xvariable gives the slope of the line, -2.Perpendicular lines have negative reciprocals for their slopes. In this case, this will be 21. 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.
b 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 21, or 0.5, and we can use the point (-1,6), so m=0.5 and (x1,y1)=(-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.
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