Question

Identifying the slope, y-intercept and x- intercept of each

Answer 1

slope= -3

y-intercept= 6

Explanation:

1. Approach

To solve this problem, one needs the slope and the y-intercept. First, one will solve for the slope, using the given points, then input it into the equation of a line in slope-intercept form. The one can solve for the y-intercept.

2.Solve for the slope

The formula to find the slope of a line is;

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Where (m) is the variable used to represent the slope.

Use the first two given points, and solve;

(1, 3), (2, 0)

Substitute in,

`((0)-(3))/((2)-(1))`

Simplify;

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

3. Put equation into slope-intercept form

The equation of a line in slope-intercept form is;

`y = mx + b`

Where (m) is the slope, and (b) is the y-intercept.

Since one solved for the slope, substitute that in, then substitute in another point, and solve for the parameter (b).

`y=-3x+b`

Substitute in point (3, -3)

`-3=-3(3)+b\\-3 = -9 + b\\6 = b`