Write the slope -intercept equation for the line with the slope-1/4 and y-intercept(0,-2) and graph the line.Show work.
Graph: (-4,-1), (0,-2), (4,-3).
Sure, I can help you with that! The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is given as -1/4, and the y-intercept is (0, -2). So we substitute these values into the equation:
y = (-1/4)x + (-2)
Simplifying, we have:
y = (-1/4)x - 2
Now, let's graph the line. To do that, we need to plot the y-intercept (0, -2), and then find one more point using the slope.
When x = 4 (which is 4 units to the right of 0), we can find the corresponding y-value:
y = (-1/4)(4) - 2
Simplifying,
y = -1 - 2
y = -3
So when x = 4, y = -3.
Now we can plot the two points: (0, -2) and (4, -3).
Join the two points with a straight line, and there you have it!
To write the slope-intercept equation for a line, we use the formula:
y = mx + b
where:
- "y" represents the dependent variable or the value of the line on the y-axis,
- "m" represents the slope of the line, and
- "b" represents the y-intercept, which is the point where the line crosses the y-axis.
In this case, the given slope is -1/4, and the y-intercept is (0, -2).
Now, let's substitute the values in the formula to find the equation:
y = (-1/4)x + (-2)
This simplifies to:
y = (-1/4)x - 2
So, the slope-intercept equation for the line is y = (-1/4)x - 2.
To graph the line, we need to plot the y-intercept at (0, -2), and then use the slope to find additional points on the line.
Start by plotting the y-intercept (0, -2) on the coordinate plane. This is the point where the line crosses the y-axis.
-2 |
|
| . (0, -2)
|
|
---------------------
0
To find more points on the line, we can use the slope. Since the slope is -1/4, this means that for every increase of 1 in the x-coordinate, the y-coordinate will decrease by 1/4.
Using this information, we can find more points by selecting values for x and calculating the corresponding y-values.
For example, if we choose x = 4, then the y-value would be:
y = (-1/4)(4) - 2
= -1 - 2
= -3
So, another point on the line is (4, -3).
Similarly, we can find more points by choosing different x-values and calculating the corresponding y-values.
Plotting the points (4, -3) and connecting them with a straight line, we get the graph of the line:
-2 |
|
| . (0, -2)
|
|
-4|
| .
| (4, -3)
-6|
---------------------
0
Given: m = -1/4. y-int. (0,-2).
Y = mx + b.
Eq: Y = (-1/4)x - 2.