
Robert S. answered 07/02/15
Tutor
New to Wyzant
Rice Univ. Grad Tutor for Chemistry, Physics, and Algebra to Calculus
Part A: In order to distinguish the two line, make the Y in (formula of) the first line a Y1 and the other Y2.
Y1= -x +2
Y2= 4x +3
Now when the two lines intersect the values for the Y's at that point must be equal. So
-x +2 = Y1 = Y2 = 4x +3
Part B: What? Make tables? Doesn't you teacher know algebra?
-x +2 = 4x +3
Isolate the x's
2-3 = 4x +x
-1 = 5x
x = -1/5 = - 0.2 ==> Y1 = Y2= -(-0.2) + 2 = 2.2
So the lines should intersect at the point (-0.2, 2.2)
Part C: To do this (easily) put both equations in slope-(y)intercept form. y = mx +b
In this form m= the slope (rise/run) and b= the y-intercept = the point on the y-axis where the line crosses the y-axis.
So for Y1= -x +2 , put a little mark on the vertical (Y) axis at +2,
now from that point, count 2 (unit spaces) to the right, then from there count down 2 spaces and put a little mark.
Now connecting those 2 points draws the first line.
For Y2= 4x+3, find 3 units up on the y-axis (mark), now from there move to the right 3 units,
From there move up 12 spaces and put a mark. I used 3 and 12 because m=4=12/3. Now connect the two marks to draw the second line.
Again, the lines should intersect at the point (-0.2, 2.2)