Answer and step-by-step explanation:
Graphing y = -2x - 6:
- y = -2x - 6 is in the slope-intercept form of a line.
- The general equation for the slope-intercept form is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Since the y-intercept is at (0, -6), mark this point on the graph.
- We can think of slope as rise over run.
- We can think of -2 as the fraction -2/1.
- Thus, a slope of -2 means that you rise (move down) -2 units each time and run (move right) 1 unit each time.
Thus, you can subtract 2 from the y-coordinate and add 1 to the x-coordinate of (0, -6) to find another point on the line.
(0 + 1, -6 - 2)
(1, -8).
Thus, mark the point (1, -8).
We can keep subtracting 2 from every y-coordinate and adding 1 to every x-coordinate until we exceed the numbers on the graph.
I'll attach a picture from the Desmos graphing calculator that shows you where to draw each point.
After you finish drawing the points, make the line by connecting the points.
Graphing x - 4y = 28:
- We can convert x - 4y = 28 to slope-intercept form by isolating y.
- We'll first need to subtract x from both sides:
(x - 4y = 28) - x
-4y = -x + 28
- Now we need to divide both sides by -4 to fully find the slope-intercept form:
(-4y = -x + 28) / -4
y = -x/-4 + 28/-4
y = 1/4x - 7
Since the y-intercept is at (0, -7), mark this point on the graph.
- A slope of 1/4 means that you rise (move up) 1 unit and run (move right) 4 units.
- Thus, you can add 1 to the y-coordinate and add 4 to the x-coordinate of (0, -7) to find another point on the line.
(0 + 4, -7 + 1)
(4, -6)
Thus, mark the point (4, -6)
We can keep adding 1 to every y-coordinate and adding 4 to every x-coordinate until we exceed the numbers on the graph.
I'll attach a picture from the Desmos graphing calculator that shows you where to draw each point.
After you finish drawing the points, make the line by connecting the points.