Respuesta :
Hello there,
1. The standard form of a straight line with a slope and a y-intercept is as follows:
[tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
In this case, we have a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of 3. Plugging in [tex]\frac{1}{2}[/tex] for [tex]m[/tex] and 3 for [tex]b[/tex] gives us:
[tex]y=\frac{1}{2}x+3[/tex]
2. We are given two points. With these two points, we can find the slope with the formula for the slope to be:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
We can use the points and the corresponding values to solve for the slope:
[tex]m=\frac{1-(-3)}{2-(-1)}=\frac{4}{3}[/tex]
We can plug [tex]m[/tex] into our equation:
[tex]y=\frac{4}{3}x+b[/tex]
To find b, we simply plug in one of our points into this equation, and solve. I will use (2, 1) since both values are positive, but feel free to use (-1, -3) if you'd like:
[tex]1=\frac{4}{3}(2)+b[/tex]
[tex]1=\frac{8}{3}+b[/tex]
[tex]-\frac{5}{3}=b[/tex]
Now plug [tex]b[/tex] into the equation.
[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex]
Hope this helps! :^)
