Solving Point-Slope Form Example Problems Made Easy

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Solving Point-Slope Form Example Problems Made Easy

Are you struggling with solving point-slope form example problems? Don't worry, we've got you covered. In this article, we'll take a closer look at the point-slope form of a linear equation and provide you with easy-to-follow steps to solve example problems.

What is the Point-Slope Form of a Linear Equation?

The point-slope form of a linear equation is a way of expressing a linear equation in terms of the slope and a point on the line. It is often used to find the equation of a line when we know the slope and a point on the line. The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

How to Solve Point-Slope Form Example Problems

Now that we've covered the basics of the point-slope form, let's move on to solving example problems. Here are the steps to follow:

1. Read the problem carefully: Read the problem carefully and identify the slope and the point on the line.
2. Write the point-slope form: Write the point-slope form of the linear equation using the slope and the point.
3. Simplify the equation: Simplify the equation by multiplying out the brackets and combining like terms.
4. Write the equation in slope-intercept form: Write the equation in slope-intercept form (y = mx + b) to make it easier to graph.

Example Problem 1

Find the equation of the line that passes through the point (2, 3) and has a slope of 4.

Solution

1. Read the problem carefully: We are given the point (2, 3) and the slope (4).
2. Write the point-slope form: y - 3 = 4(x - 2)
3. Simplify the equation: y - 3 = 4x - 8
4. Write the equation in slope-intercept form: y = 4x - 5

Example Problem 2

Find the equation of the line that passes through the point (-1, 2) and has a slope of -3.

Solution

1. Read the problem carefully: We are given the point (-1, 2) and the slope (-3).
2. Write the point-slope form: y - 2 = -3(x + 1)
3. Simplify the equation: y - 2 = -3x - 3
4. Write the equation in slope-intercept form: y = -3x - 1

Example Problem 3

Find the equation of the line that passes through the points (1, 2) and (3, 4).

Solution

1. Read the problem carefully: We are given two points on the line.
2. Find the slope: The slope is given by m = (y2 - y1)/(x2 - x1) = (4 - 2)/(3 - 1) = 1
3. Write the point-slope form: y - 2 = 1(x - 1)
4. Simplify the equation: y - 2 = x - 1
5. Write the equation in slope-intercept form: y = x + 1

Conclusion

Solving point-slope form example problems is a straightforward process once you understand the basics of the point-slope form. By following the steps outlined in this article, you'll be able to solve even the most challenging point-slope form example problems with ease.