slope intercept form from a table calculator

Since we know the slope, we can start with the second step and input 1/2 for the m variable, 5 for the x variable, and 6 for the y variable to solve for b using slope-intercept form.

The result is the equation of the line in slope-intercept form.įor example, let’s create the equation for a line with a slope of 1/2 and a point (5, 6) in slope-intercept form. Now, input the slope and y-intercept for the m and b variables in the slope-intercept form equation. Step Three: Express the Line in Slope-Intercept Form You can also find b using a y-intercept calculator. Input the slope and coordinates for a known point on the line for the m, x, and y variables, respectively, in the slope-intercept form equation. If you know the slope already, then you can skip this step. If you know two points on the line, you can use the slope formula above to find it or use a slope calculator. The first step is to find the line’s slope. You can express the equation of a straight line in slope-intercept form in a few steps.

Then, since point (x 2, y 2) is an arbitrary point on the line, we can rename it to just (x, y).įinally, we see that the resulting equation of the line is the slope-intercept form equation above. Now, we can substitute the y-intercept (which, by definition, is the coordinate (0, b)) for (x 1, y 1). If you multiply both sides of this equation by the denominator (x 2 – x 1), the formula can be rewritten as: The formula for slope using the coordinates for two points (x 1, y 1) and (x 2, y 2) is: Slope-intercept form is derived from the slope formula. In the slope-intercept formula, the slope of the line m is the coefficient for the x-coordinate, and the y-intercept is represented as the b variable. The slope-intercept form of a line states that the y-coordinate y of a point on the line is equal to the slope m times the x-coordinate x plus the y-intercept b. The slope-intercept form equation is given by: The y-intercept is the y-coordinate where the line crosses the y-axis. Slope-intercept form is applicable when you have the slope and y-intercept for a line or when you can calculate these for the line. The combination of these elements can be used to plot any point on the line. Slope-intercept form gets its name because the equation contains the slope and the y-intercept of the line. The slope-intercept form equation can be used to find any point on the line. Slope-intercept form is a type of linear equation format used to express a straight line. Slope-intercept form is probably the most frequently used equation format to represent a line, but you can also express the line in point-slope form or standard form. You can use a calculator like the one above to find the equation for a straight line in slope-intercept form, but you can also follow the steps below to find it. The most commonly used method is an algebraic equation in slope-intercept form.

Students, now must slide the line to match it with the green segment.There are several ways to describe a line using its slope, or gradient.

The orange line covering the red line proves that the 2 equations are equal. This is a great situation to highlight when presented in class. One reduce (red) and the other not (orange).

In the graphic, you can see two forms of the equation.

pick either point (2, -7) or (8, -4) to substitute into (x, y).

Substitute to solve for the y-intercept: y = mx + b.

Use slope formula to calculate the rate of change.

Now that the students know the answer, they can use that answer to guide their calculations.

Ask students to move the new line (red) so it covers the green segment.

Ask students to enter the equation y = 1/2x.

Ask students to press the button to connect the points.

Ask them to state an observation for the y-intercept.

Ask them to state an observation for the slope.

Ask students to enter in the points into the table.

Desmos provides a visual! Our visual learners can glean more understanding of linear equations than expected if we incorporate interactive visual tools such as Desmos. I’ll have a hard copy of my notes and then I can share them with multiple people. As I drafted notes, I thought, “Why not write the steps in my blog”. One of my teachers asked me to incorporate a different perspective on writing a line in slope-intercept form when given two points.

Slope intercept form from a table calculator