A line's equation is usually expressed as y = mx + b, where m is the slope and b is the y-intercept. This article will teach you how to get the equation of a line given a point through which the line passes and its slope. Before we begin, it may help to know what a line's slope is. The slope of a line is defined as the ratio of any two of **its coordinates**; in other words, it is the change in the value of **the first coordinate** divided by the change in the value of the second coordinate.

As an example, let's say that we want to find the equation of the line that goes through the point (4, 8) and has a slope of 2. We can use the formula y - y1 = m(x - x1), where m is the slope and x1 and y1 are the coordinates of some point on the line. In this case, since the line has a slope of 2, then it should be able to be described by a factor of 2: any change in y should be followed by a change in x of twice that amount. 4 - 8 = -4, so the y-coordinate of our point will be -4m. Since the line goes through the point (4, 8), then its x-coordinate will be 4, so x1 = 4.

Expert Tutors Provide 2 Answers The slope-intercept version of **the line equation** is: y = mx + b, where m is the slope. If we let x = 6, then y = 3m + B. Setting these two equations equal to each other gives us **a linear equation** that can be solved for m and b: m = -3y/6x and b = 3mx + C. Therefore, the slope-intercept form of the equation of the line through (6, 3) with a slope of -3 is: y = -3x + 9.

The point-slope form of the equation of the line passing through (6, 3) with a slope of -3 is: y - 3x = 9. This can also be written as: y - x*3 = 9 which means the line passes through the origin and has a negative slope.

To get the slope of a line given **its equation**, write it in slope-intercept form first. In order to write y=mx+b, use **inverse operations** to solve for Y. The slope is therefore immediately visible since it is the coefficient of the x variable, or the number in front of X.

The formula for finding the slope of a line is: m = (y2-y1)/(x2-x1). This can be rewritten as m = (y-y1)/(x-x1), where y-y1 and x-x1 are called "slopes". A line with a negative slope will describe a downward angle while one with a positive slope will describe **an upward angle**. Lines that go through the origin are called "vertical" lines because they don't tell us anything new about the data they're drawn on; they're just straight lines.

If you have two equations that represent the same line, then they have the same slope. This is important to remember when trying to find the slope of a line using information from only two points on the line.

For example, if you have y=mx+b and x=3, then b=y-3*m. Since this holds for **any value** of m, we can say that b does not depend on m.

How to Calculate the Slope-Intercept Form So, recall, our equation is: y = mx + bm, where m represents the slope and b represents the line's y-intercept. To calculate the slope-intercept form, first take the derivative of the function with respect to x. In this case, we are taking the derivative with respect to t. This means that we need to find dt/dx. It is easier to divide both sides by dx: dt/dx = (dy/dx)/(dx/dt). Now, we can set this equal to m and solve for t: m = (dy/dx)/(dx/dt). Plugging in some numbers, we get: m = (8x - 16) / (1 - 2x), which reduces to 8m = 16 - 4x, or m = 4 if you simplify. Now that you know the slope, you can use it with your intercept to create a new point on the curve.

As you can see, there are many ways to calculate **the slope-intercept form**. The main thing is that you need to be clear on what type of equation you are trying to create before you start solving for m and b. If you aren't sure how to approach these problems, try using **some simple examples** until you understand the process required to solve them.