The slope is found by \(y_{2} -y_{1} / x_{2} - x_{1}\)
Line 1: y2 is 6, y1 is 4, x2 is 2, x1 is -2
6-4/2- -2= 2/4=1/2
Slope intercept is written as y= mx+b. m is the slope, and b is the intercept (the intercept is the value of y when x is 0). To find out the intercept, we plug in values of y, m and x
4= 1/2(-2) +b
4=-1+b
5=b
The equation for line 1 is y= 1/2x +5
Using the same formulas as above, the equation for line 2 is y= 3x+4
The solution to the system is a point where both lines would meet in the graph, or a set of x and y values that satisfies both equations.
y= 3x+4
y= 1/2x+5
3x+4 = 1/2x+5
3x= 1/2x +5 -4
3x= 1/2x +1
3x-1/2x= 1
2.5x=1
2.5x/2.5=1/2.5
x=0.4
Plug 0.4 into the slope intercept equation
y= 3(0.4) +4
y= 1.2 +4
y=5.2
y= 1/2(0.4) +5
y= 0.2 +5
y= 5.2
The solution is 0.4, 5.2
The other set of lines
Line 1: y= 3x+2
Line 2: y= -2x +7
Solution: 1,5
