Question

What is the slope and y-intercept of this line `2x+y=7`?

Answer 1

slope = - 2
y-intercept = 7

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(bar(ul(|color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b may be extracted ' easily'.

`2x+y=7" can be expressed in this form"`

subtract 2x from both sides.

`cancel(2x)cancel(-2x)+y=7-2x`

`rArry=-2x+7" is now in slope-intercept form"`

Thus `"slope" =-2" and y-intercept" =7`
graph{-2x+7 [-14.24, 14.24, -7.12, 7.12]}