One
Slope
The general slope intercept equation for a line is
y = mx + b
If you are told outright what the slope is then you can write m = slope in this case - 3
So you have so far is y = -3x + b. Now you use the point to get the y intercept.
(2,5) means that when x = 2, y = 5. that allows you to solve for b
Y intercept
When x = 2, y = 5. Substitute that into the general equation with the slope.
5 = -3x + b Put 2 in for x
5 = -3 * 2 + b Multiply -3 * 2
5 = - 6 + b Add 6 to both sides
5 + 6 = b
11 = b
Answer
y = -3x + 11
Two
This question is a little harder. You have to find the slope.
Slope Formula
[tex]\text{m = } \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Givens
Points (2, -1), (-6, - 5)
y2 = -1 ; y1 = -5; x2 = 2; x1 = -6
Solve
m = (-1 - - 5)/(2 - - 6) = (-1 + 5)(2 + 6) = 4/8 = 1/2
Now find the y intercept. Use either one of the given points
(2,-1) when x = 2, y = - 1
y = 1/2 x + b Show what you have so far. Put in x = 2 for x and y = - 1 for y
-1 = 1/2(2) + b Multiply 2*1/2
-1 = 1 + b Subtract 1 from both sides.
-1 -1 = b
- 2 = b
Answer
y = (1/2)x - 2 which is D
