Question

What is the slope-intercept equation of the line below?

Answer 1

y= 2x - 3

Explanation:

To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.

Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.

• slope =
`(y_(2) - y_(1) )/(x_(2) - x_(1))`

=
`(3 - (-1))/(3 - 1)`

=
`(4)/(2)`

= 2

The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.

• intercept = -3

The slope-intercept equation of a line takes the form:

y = mx + c

where 'm' is the slope and 'c' is the y-intercept.

Substituting the values we found into the equation gives us:

y = 2x + (-3)

∴ y = 2x - 3