Line AB Passes Through Points A(-6, 6) And B(12, 3). If The Equation Of The Line Is Written In Slope-intercept Form $y = Mx + B$, Then Find The Values Of M And B.What Is The Value Of B?A. 5 B. -5 C. 6

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Introduction

In mathematics, the slope-intercept form of a line is a way to express the equation of a line in the form y=mx+by = mx + b, where mm is the slope of the line and bb is the y-intercept. In this article, we will explore how to find the values of mm and bb for a given line that passes through two points.

The Slope-Intercept Form of a Line

The slope-intercept form of a line is given by the equation y=mx+by = mx + b, where:

  • mm is the slope of the line
  • bb is the y-intercept of the line

The slope of a line is a measure of how steep the line is, and it can be calculated using the formula:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two points on the line.

Finding the Slope of the Line

In this problem, we are given two points on the line: A(−6,6)A(-6, 6) and B(12,3)B(12, 3). We can use these points to calculate the slope of the line using the formula above.

def calculate_slope(x1, y1, x2, y2):
    return (y2 - y1) / (x2 - x1)

x1, y1 = -6, 6
x2, y2 = 12, 3

slope = calculate_slope(x1, y1, x2, y2)
print(slope)

When we run this code, we get a slope of 3−612−(−6)=−318=−16\frac{3 - 6}{12 - (-6)} = \frac{-3}{18} = -\frac{1}{6}.

Finding the Y-Intercept of the Line

Now that we have the slope of the line, we can use one of the points to find the y-intercept of the line. We will use point A(−6,6)A(-6, 6).

We can plug in the values of xx and yy into the equation y=mx+by = mx + b and solve for bb.

def calculate_y_intercept(slope, x, y):
    return y - slope * x

slope = -1/6
x, y = -6, 6

y_intercept = calculate_y_intercept(slope, x, y)
print(y_intercept)

When we run this code, we get a y-intercept of 6−(−16)(−6)=6−1=56 - (-\frac{1}{6})(-6) = 6 - 1 = 5.

Conclusion

In this article, we have seen how to find the equation of a line in slope-intercept form using two points on the line. We have also seen how to calculate the slope and y-intercept of the line using the formulae above. In this problem, we have found that the slope of the line is −16-\frac{1}{6} and the y-intercept is 55.

The Final Answer

Introduction

In our previous article, we explored how to find the equation of a line in slope-intercept form using two points on the line. We also calculated the slope and y-intercept of the line. In this article, we will answer some frequently asked questions related to the equation of a line in slope-intercept form.

Q: What is the slope-intercept form of a line?

A: The slope-intercept form of a line is a way to express the equation of a line in the form y=mx+by = mx + b, where mm is the slope of the line and bb is the y-intercept of the line.

Q: How do I calculate the slope of a line?

A: To calculate the slope of a line, you can use the formula:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two points on the line.

Q: How do I calculate the y-intercept of a line?

A: To calculate the y-intercept of a line, you can use the formula:

b=y−mxb = y - mx

where mm is the slope of the line, xx is the x-coordinate of a point on the line, and yy is the y-coordinate of the same point.

Q: What is the difference between the slope and the y-intercept?

A: The slope of a line is a measure of how steep the line is, while the y-intercept is the point where the line intersects the y-axis.

Q: Can I use any two points to calculate the equation of a line?

A: Yes, you can use any two points to calculate the equation of a line. However, you should make sure that the two points are not the same point, as this would result in a line with zero slope.

Q: How do I write the equation of a line in slope-intercept form if I know the slope and the y-intercept?

A: If you know the slope and the y-intercept of a line, you can write the equation of the line in slope-intercept form as:

y=mx+by = mx + b

where mm is the slope of the line and bb is the y-intercept of the line.

Q: Can I use the equation of a line in slope-intercept form to find the x-coordinate of a point on the line?

A: Yes, you can use the equation of a line in slope-intercept form to find the x-coordinate of a point on the line. To do this, you can plug in the values of yy and mm into the equation and solve for xx.

Conclusion

In this article, we have answered some frequently asked questions related to the equation of a line in slope-intercept form. We have also seen how to calculate the slope and y-intercept of a line using two points on the line. We hope that this article has been helpful in understanding the concept of the equation of a line in slope-intercept form.

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