Question

Write all equations in slope-intercept form ,standard form and find the x and y intercept

Answer 1

The Slope-Intercept form of an equation of a line, is:

`y=mx+b`

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:

`\begin{gathered} x=-1 \\ y=3 \\ m=2 \end{gathered}`

Substitute these values into the equation and solve for "b":

`\begin{gathered} 3=2(-1)+b \\ 3=-2+b \\ 3+2=b \\ b=5 \end{gathered}`

Knowing "m" and "b", you can determine that the Slope-Intercept form of the equation of this line, is:

`y=2x+5`

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:

`\begin{gathered} 0=2x+5 \\ -5=2x \\ (-5)/(2)=x \\ x=-2.5 \end{gathered}`

The Standard form of the equation of a the line, is:

`Ax+By=C`

Where "A", "B" and "C" are Integers ("A" must be positive).

So, the Standard form of this equation is:

`\begin{gathered} y=2x+5 \\ -5=2x-y \\ 2x-y=-5 \end{gathered}`

Therefore, the answers are:

a) Slope-Intercept form:

`y=2x+5`

b) Standard form:

`2x-y=-5`

c) x-intercept:

`x=-2.5`

d) y-intercept:

`b=5`