Answer:
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is [tex]y -y_{1} =m(x -x_{1})[/tex] where we substitute a point (x,y) for [tex](x_{1},y_{1})[/tex].
We do not have m for the slope. But we do have (1,-2) and (-3, 4). We input the points for [tex]x_{1} =1\\y_{1}=-2[/tex] and [tex]x=-3\\y=4[/tex].
[tex](4-(-2))=m (-3-1)[/tex]
We now simplify the parenthesis and solve for m.
[tex](4+2)=m (-3+-1)\\6=m(-4)=[/tex]
We divide by -4 on both sides and find [tex]m=-\frac{6}{4} =-\frac{3}{2}[/tex]. We substitute m into the point slope form with one coordinate pair.
[tex]y-(-2)=-\frac{3}{2}(x-1)\\y+2=-\frac{3}{2}(x-1)\\y+2=-\frac{3}{2}x+\frac{3}{2}\\y+2-2=-\frac{3}{2}x+\frac{3}{2}-2\\y=-\frac{3}{2}x+\frac{3}{2}+\frac{4}{2} \\y=-\frac{3}{2}x+\frac{7}{2}[/tex]
After simplifying the parenthesis, we subtracted 2 from both sides. We converted 2 into a fraction with 2 as the denominator.
This is slope intercept form[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]. The line has slope -3/2 and y-intercept (0,7/2) or b=7/2.
