Find The Equation Of The Line Specified.The Slope Is 6, And It Passes Through { (-4, 4)$}$.A. { Y = 6x + 4$}$B. { Y = 6x - 20$}$C. { Y = 12x + 28$}$D. { Y = 6x + 28$}$Please Select The Best Answer From
Introduction
In mathematics, the equation of a line is a fundamental concept that is used to describe the relationship between two variables. Given the slope and a point on the line, we can find the equation of the line using the point-slope form. In this article, we will explore how to find the equation of a line specified by its slope and a point it passes through.
The Point-Slope Form
The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope. This form is useful when we know the slope and a point on the line.
Given Information
We are given that the slope (m) is 6 and the line passes through the point (-4, 4). We need to find the equation of the line.
Using the Point-Slope Form
Substituting the given values into the point-slope form, we get:
y - 4 = 6(x - (-4))
Simplifying the equation, we get:
y - 4 = 6(x + 4)
Expanding the right-hand side, we get:
y - 4 = 6x + 24
Adding 4 to both sides, we get:
y = 6x + 28
Comparing with the Options
Now, let's compare the equation we found with the options given:
A. y = 6x + 4 B. y = 6x - 20 C. y = 12x + 28 D. y = 6x + 28
The equation we found matches option D.
Conclusion
In this article, we learned how to find the equation of a line specified by its slope and a point it passes through. We used the point-slope form of a line and substituted the given values to find the equation. We then compared the equation with the options given and found that the correct answer is option D.
Final Answer
The final answer is:
Q: What is the point-slope form of a line?
A: The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Q: How do I find the equation of a line using the point-slope form?
A: To find the equation of a line using the point-slope form, you need to substitute the given values into the equation. The given values include the slope (m) and a point (x1, y1) on the line.
Q: What if I don't know the slope of the line? Can I still find the equation?
A: Yes, you can still find the equation of the line even if you don't know the slope. You can use the slope-intercept form of a line, which is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Q: How do I find the y-intercept (b) of a line?
A: To find the y-intercept (b) of a line, you need to substitute the given values into the slope-intercept form of a line. The given values include the slope (m) and a point (x1, y1) on the line.
Q: Can I use the point-slope form to find the equation of a horizontal line?
A: Yes, you can use the point-slope form to find the equation of a horizontal line. A horizontal line has a slope of 0, so the equation will be in the form:
y = c
where c is a constant.
Q: Can I use the point-slope form to find the equation of a vertical line?
A: Yes, you can use the point-slope form to find the equation of a vertical line. A vertical line has an undefined slope, so the equation will be in the form:
x = c
where c is a constant.
Q: What if I have two points on the line? Can I still find the equation?
A: Yes, you can still find the equation of the line even if you have two points on the line. You can use the two-point form of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Q: How do I find the slope (m) of a line using two points?
A: To find the slope (m) of a line using two points, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Conclusion
In this article, we answered some frequently asked questions about finding the equation of a line. We covered topics such as the point-slope form, slope-intercept form, and two-point form. We also discussed how to find the slope and y-intercept of a line using different methods.