The Slope-Intercept form of an equation of a line, is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" the y-intercept.
You know that this line passes through the point (-1,3) and its slope is 2. Then:
[tex]\begin{gathered} x=-1 \\ y=3 \\ m=2 \end{gathered}[/tex]
Substitute these values into the equation and solve for "b":
[tex]\begin{gathered} 3=2(-1)+b \\ 3=-2+b \\ 3+2=b \\ b=5 \end{gathered}[/tex]
Knowing "m" and "b", you can determine that the Slope-Intercept form of the equation of this line, is:
[tex]y=2x+5[/tex]
Since the value of "y" is zero when a line intersects the x-axis, you can substiute that value into the equation in Slope-Intercept form and solve for "x", in order to find the x-intercept:
[tex]\begin{gathered} 0=2x+5 \\ -5=2x \\ \frac{-5}{2}=x \\ x=-2.5 \end{gathered}[/tex]
The Standard form of the equation of a the line, is:
[tex]Ax+By=C[/tex]
Where "A", "B" and "C" are Integers ("A" must be positive).
So, the Standard form of this equation is:
[tex]\begin{gathered} y=2x+5 \\ -5=2x-y \\ 2x-y=-5 \end{gathered}[/tex]
Therefore, the answers are:
a) Slope-Intercept form:
[tex]y=2x+5[/tex]
b) Standard form:
[tex]2x-y=-5[/tex]
c) x-intercept:
[tex]x=-2.5[/tex]
d) y-intercept:
[tex]b=5[/tex]
