Question

How do you graph using the intercepts for `-2x+y=3`?

Answer 1

`color(blue)(y_("intercept") = 3)" "color(blue)(x_("intercept")=-1.5)`

Mark these points on the axis and draw a straight line through them.

Explanation:

Given:`" "color(brown)( -2x+y=3)`

Change this into the standard format of `y= mx+c`

Add `color(blue)(2x)` to both sides

`color(brown)(color(blue)(2x)-2x+y" "=" "3color(blue)(+2x)`

`0+y=2x+3`

`y=2x+3`............................(1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the y intercept")`

If you look at the graph the plotted line crosses the y-axis when `x=0`

So substitute `color(green)(x=0)` into equation (1)

So `y=2x+3" becomes " y= 2(color(green)(0))+3`

that is:`" "y=(2xxcolor(green)(0))+3" " =" " 0 + 3`

So `color(red)(y_("intercept") = 3)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the x intercept")`

If you look at the graph the plotted line crosses the x-axis when `y=0`

So substitute `color(green)(y=0)` into equation (1)

So `color(brown)(y=2x+3)" becomes " color(brown)(color(green)(0)= 2x+3)`

Subtract `color(blue)(3)` from both sides

`color(brown)(color(green)(0)color(blue)(-3)= 2x+3color(blue)(-3))`

`-3=2x+0`

`color(brown)(2x=-3)`

Divide both sides by 2 which is the same as `color(blue)(xx1/2)`

`color(brown)(color(blue)(1/2xx) 2x=color(blue)(1/2xx)(-3)`

`2/2 x=-3/2`

But `2/2 = 1` giving:

`x=-3/2 -> -1 1/2 -> -1.5`

`color(red)(x_("intercept")=-1.5)`