Answer:
DHGB
Step-by-step explanation:
Let's start with 1.
The equation is in standard form (ax+by=c): -4x+2y=8
we'll put it into slope intercept form.
Add 4x onto both sides
2y=4x+8
divide by 2
y=2x+4
Parallel lines have the same slope, but a different y intercept. (the line parallel to this one will have a slope of 2 but a y intercept different from +4)
Looking at the answer choices, the only choice with a slope of 2 is D (y=2x-5)
So the answer to 1 is D
Now 2.
we're given 3 points. One of the points crosses the y axis, which is the y intercept. In this case, the line crosses the point (0,3)
That means the y intercept of the line is (0,3)
here's the line so far:
y=mx+3 (m is a placeholder for the slope)
when given a graph, we can use rise/run. Starting from the point (3,2), we can move 3 spaces to the left, and one up.
In a graph, if you move to the left or downwards, it's a negative move. If you move up or to the right, it's a positive move.
Since we went 1 space up (rise) and 3 spaces to the left, (run) the slope is -1/3
So the line is y=-1/3x+3
Perpendicular lines are negative and reciprocal. If you multiply their slopes, they will equal -1. Their y intercepts don't matter at all.
So to find the slope, we can use this equation.
-1/3m=-1
multiply by -3 on both sides
m=3
Looking at the answer choices, H is the only answer with a slope of 3. So the answer to 2 is H.
Now, 3
You can do the graph method like above for 2, but I'll just calculate the slope.
We're given two points, (-1,-2) and (0,2)
the formula for slope is (y2-y1)/(x2-x1)
we can label the points.
x1=-1
y1=-2
x2=0
y2=2
now, substitute into the equation.
m=(2--2)/(0--1)
m=4/1
the slope is 4.
Now let's use point slope form, which is y-y1=m(x-x1)
once again, sub. into the equation.
y+2=4(x+1)
do distributive prop
y+2=4x+4
subtract by 2
y=4x+2
As said above, parallel lines have the same slope.
Looking at the answer options, G also has the slope of 4
so the answer to 3 is G
Finally, #4
Equation: 3x+y=1
subtract 3x from both sides
y=-3x+1
As said above, perpendicular lines have slopes that multiply to equal -1.
-3m=-1
multiply by -1/3
m=1/3
so the slope of the line will be 1/3.
Looking at the answer options, B also has a slope of 1/3.
So the answer to 4 is B
The code is DHGB
Hope this helps!
