Answer:
y=-3x+4
Step-by-step explanation:
Just plug in y=mx+b
Slope intercept form of line passing through (4, 0) and (0, 8) that means slope intercept form of line having x-intercept of 4 and a y-intercept of -3 is [tex]y=\frac{3}{4} x-1[/tex].
Solution:
Need to find the equation of a line in slope intercept form
Given that,
x intercept of line is 4 and y intercept of line = -3 ; x intercept is a point where line crosses the x axis.
In our case line have x intercept of 4, which means line crosses x axis at 4. Another catch here is at x axis, value of y is always 0. So we can say that line passes through point (4, 0).
y intercept is a point where line crosses the y axis. In our case line have y intercept of -3 , which means line crosses y axis at -3.Also at y axis, value of x is always 0.
So we can say that line passes through point (0,-3). Now we can say that we need equation of line passing through (4, 0) and (0, -3)
Equation of line passing through point [tex](x_1, y_1) \ and \ (x_2, y_2)[/tex] is given by
[tex]y-y_{1}=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}\left(x-x_{1}\right) \rightarrow(1)[/tex]
In our case [tex]x_1 = 4; \ y_1=0; \ x_2 = 0; \ y_2 = -3[/tex]
Substituting given value in (1) we get ,
[tex]\begin{array}{l}{y-0=\frac{(-3-0)}{(0-4)}(x-4)} \\\\ {\Rightarrow y=\frac{3}{4}(x-4)} \\\\ {\Rightarrow y=\frac{3}{4} x-1}\end{array}[/tex]
Hence slope intercept form of line passing through (4, 0) and (0, 8) is [tex]y=\frac{3}{4} x-1[/tex]
