Interpreting Lines:This is an introduction to drawing lines when given the slope and the y-intercept in an equation form. Remember that the y-intercept is where the graph crosses the y-axis; this is where we usually start. First, find the y-intercept, then determine the slope. For now, just focus on whether the slope is positive or negative. Show Here are the variables we will start using in our function:
The equation is y = mx + b. The x and y variables remain as letters, but m and b are replaced by numbers (ex: y = 2x + 4, slope = 2 and y-intercept = 4). The following video will show a few examples of understanding how to use the slope and intercept from an equation. Video Source (03:53 mins) | Transcript y = mx + b This equation is called the slope-intercept form because the two numbers in the equation are the slope and the intercept. Remember, the slope (m) is the number being multiplied to x and the intercept (b) is the number being added or subtracted. Additional Resources
Practice Problems
The equation, y = mx + b, is the slope-intercept form of a straight line. Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis. The equations of lines can be of different forms based on the information we have. Suppose the coordinates of two points are given, which forms a straight line, then the line will form a linear equation
(e.g. y = x + 3, where x and y are the coordinates of the point). The general form of the equation of the straight line is given by Ax + By + C = 0, for a line. y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. x and y represent the distance of the line from the x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the
line is. The slope of the line is also called the gradient. The formula to find the slope, m, of the line is given by: m = (difference in y coordinates)/(difference in x coordinates) \(\begin{array}{l}m = \frac{y_2-y_1}{x_2-x_1}\end{array} \) The equation of a line passing through a point (x1, y1) is given by: y – y1 = m(x – x1) The equation of a line passing through two points (x1, y1) and (x2, y2) is given by: \(\begin{array}{l}\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}\end{array} \) How To Find y = mx + b?To find the equation of the straight line, we use the slope-intercept form, y = mx + b, where m is the slope of the line, b is the y-intercept of the line. We can find the equation of a line in the form of y = mx + b, if the coordinates of points forming the line are known to us. The slope of the line, m can also be written as: m = (y-b)/x So, the formula to find the slope of the straight line is: m = change in y/change in x Now, suppose we have two points on a straight line whose coordinates are (x1, y1) and (x2, y2). Thus, we can write: y1 = mx1 + b and y2 = mx2 + b Since, m is the ratio of change in y to change in x, thus; \(\begin{array}{l}\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{(m x_{2}+b)-(m x_{1}+b)}{x_{2}-x_{1}}\end{array} \) \(\begin{array}{l}=\frac{m x_{2}-m x_{1}}{x_{2}-x_{1}}\end{array} \) Taking m common, we get, \(\begin{array}{l}=\frac{m( x_{2}- x_{1})}{x_{2}-x_{1}}\end{array} \) = m Hence, \(\begin{array}{l}m = \frac{y_2-y_1}{x_2-x_1}\end{array} \) I.e., m= Difference in y coordinates / Difference in x coordinates. Y = mx + b at OriginThe equation of a straight line with slope m passing through the origin (0,0) is given by: y = mx Hence, the y-intercept at the origin is zero. Solved ExamplesExample 1: Find the slope and y-intercept of the equation, y = 3x – 2. Solution: If we compare the given equation with y = mx + b, where m is the slope and b is the y-intercept, then we get, Slope, m = 3 y-intercept, b = -2 Example 2: What is the slope and y-intercept of the equation, y= 5x? Solution: If we compare the given equation with y = mx + b, where m is the slope and b is the y-intercept, then we get, Slope, m = 5 y-intercept, b = 0 Here, the y-intercept is zero, which proves that the slope of the line passes through the origin. Example 3: If the slope of a straight line is 5 and the y-intercept is 3, then find the equation of the line. Solution: We know the equation of the line in slope-intercept form is given by: y = mx + b Given, m = 5 and b = 3. Thus, the required equation is: y = 5x + 3 How do you find the slope of the equation in Y MX B form?As we discussed in the earlier sections, in y = mx + b, 'm' represents the slope of the equation. To find the slope of a line, given its equation, we have to rearrange its terms to the slope-intercept form y = mx + b. Here, 'm' gives the slope and 'b' gives the y-intercept of the equation.
What is formed by the equation y MX B?Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.
What part of Y MX B is the yIn the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).
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