-1/2x + y = 10. I have to do some stupid slope-intercept form.
The Correct Answer and Explanation is:
To write the equation –½x + y = 10 in slope-intercept form, we need to rearrange it into the form:y=mx+by = mx + by=mx+b
where:
- m is the slope of the line, and
- b is the y-intercept (the point where the line crosses the y-axis).
Step-by-step Solution:
We start with the equation:−12x+y=10- \frac{1}{2}x + y = 10−21x+y=10
To write this in slope-intercept form, isolate y:y=12x+10y = \frac{1}{2}x + 10y=21x+10
That’s it! The equation is now in slope-intercept form:y=12x+10\boxed{y = \frac{1}{2}x + 10}y=21x+10
Explanation (Like in the textbooks):
The slope-intercept form of a linear equation is used to graph lines easily and understand how the variables relate to each other. The general formula is:y=mx+by = mx + by=mx+b
Here, m represents the slope—how steep the line is—and b represents the y-intercept, the value of y when x = 0.
In the equation –½x + y = 10, the variable y is already by itself on one side, but the x term is not yet in the form we want. To solve this, we simply add ½x to both sides of the equation to move it over. That gives:y=12x+10y = \frac{1}{2}x + 10y=21x+10
Now the equation is in the desired slope-intercept form. From this, we can directly identify:
- The slope (m) is ½, which means for every 2 units you move horizontally, the line rises by 1 unit.
- The y-intercept (b) is 10, which means the line crosses the y-axis at (0, 10).
This form is very useful in algebra for graphing and analyzing linear relationships.
