Answer:
[tex]y=\frac{3}{4}x+-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 have m=3/4 and (4, 1). We input m and [tex]x_{1} =4\\y_{1}=1[/tex].
[tex]y-1=\frac{3}{4} (x-4)[/tex]
We now simplify the parenthesis and solve for y.
[tex]y-1=\frac{3}{4} (x-4)\\y-1=\frac{3}{4}x+\frac{3}{4} (-4)[/tex]
We convert -4 into a fraction with 1 as the denominator.
[tex]y-1=\frac{3}{4}x+\frac{3}{4} (\frac{-4}{1} )\\y-1=\frac{3}{4}x+\frac{-12}{4}\\y-1=\frac{3}{4}x+-3[/tex]
We add 1 to both sides to isolate y,
[tex]y-1+1=\frac{3}{4}x+-3+1\\y=\frac{3}{4}x+-2[/tex]
This is slope intercept form. The line as slope 3/4 and y-intercept (0,2) or b=2.
