![]() Here is a two minute video showing how to do the above four steps to graph a line which is in y = mx + b form. Join the two dots with a line including arrow ends,and then write the equation of the line next to the line. If we have 3x, write the Gradient as 3/1).įrom the Y-intercept, move UP (or DOWN if negative), and then Across, and make another dot on the Grid.Ĥ. Take the value in front of “x” as the Gradient, and write it as an UP/Across fraction. Line up the equation with y = mx + b and read off the Y-Intercept as the number matching up with “b”.ĭot in this y intercept value as a point on the Y-axis.ģ. Rule up and Label an X-Y Cartesian GridĢ. There are four steps to making the Straight Line Graph:ġ. We replace the “m” and the “b” in y = mx + b with our values taken from the graph. We then substitute these values for “m” and “b” in the y = mx + b equation.Įg. If we are given a Line Graph, we can read off the Y-Intercept and Calculate the Gradient Slope. Here are a couple of examples of Rearranging into y = mx + b form. We can then find the Gradient Slope, and the Y-Intercept, without having to draw any graphs. Here is a video which shows how to rearrange equations into y = mx + c form, by applying opposite operations to both sides We do this by solving the equation for “y” Often we have equations such as 5x + 3y = 15, we need to rearrange the equation into y = mx + b format. The number or fraction value on the end of the equation is the Y-Intercept. ![]() We simply take the number or fraction value in front of “x”, and this is the Gradient Slope. If we are given a Line Equation in y = mx + b form, we can find the Slope and Y-Intercept, without drawing any graphs. Image Copyright 2013 by Passy’s World of Mathematics Let’s begin by looking at what is Gradient-Intercept Equation Form.ĭepending on what country you are in, the equation may vary, but in both formats it says that the value of every Y-Coordinate can be found by taking the X-Coordinate multiplied by the Gradient Slope and then adding on the Y-Intercept value. There are many other important Straight Line Relationships in Real Life, as shown in our previous lessons at the links below:Īs you can see, it is a big lesson containing several related items, and so work through everything very carefully, and make sure you watch the Videos. This baby was born 20 inches long (y-intercept), and has been growing at a rate of a 1/4 inch per week. Since the line is passing through the origin (0,0), there is no y-intercept or y-intercept = 0.Babies usually follow a straight line of increasing body length as they start growing. Find the equation of the line in slope intercept form.įine the slope of the line using the points (0, 0) and (-1, -8). So, the equation of the line in slope-intercept form isĪ line is passing through the points (0, 0) and (-1, -8). Since the y-coordinate at this point is 4, y-intercept is 4. So, the line intersects y-axis at this point. In the point (0, 4), x-coordinate is zero. Find the equation of the line in slope intercept form.įine the slope of the line using the points (2, 3) and (0, 4). Solved ProblemsĪ line is passing through the points (2, 3) and (0, 4). So, the y-intercept b is 0, and y = mx + b becomes y = mx. Explain your reasoning.īecause the origin is on the y-axis, the graph crosses the y-axis at (0, 0). Write the equation with y on the left side.Ĭritical thinking : Write the equation of a line with slope m that passes through the origin. In an equation of a line, we often want y by itself on one side of the equation. Slope m = change in y-values / change in x-values Complete the equation for the slope m of the line using the y-intercept (0, b), and another point (x, y) on the line. Recall that slope is the ratio of change in y to change in x. The coordinate of x is 0 in the point that includes the y-intercept. Circle the point that must be on the line. Let L be a line with slope m and y-intercept b. Let us see see, how to derive the slope-intercept form equation of a straight through the following steps. Equation of a straight line in slope-intercept form :
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