Answer:
slope= -3
y-intercept= 6
Step-by-step 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;
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where (m) is the variable used to represent the slope.
Use the first two given points, and solve;
(1, 3), (2, 0)
Substitute in,
[tex]\frac{(0)-(3)}{(2)-(1)}[/tex]
Simplify;
[tex]\frac{-3}{1}\\\\=-3[/tex]
3. Put equation into slope-intercept form
The equation of a line in slope-intercept form is;
[tex]y = mx + b[/tex]
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).
[tex]y=-3x+b[/tex]
Substitute in point (3, -3)
[tex]-3=-3(3)+b\\-3 = -9 + b\\6 = b[/tex]
