To write the equation of a line in slope-intercept form, which is expressed as y = mx + b, you need to know the slope (m) and a point on the line. Here’s a step-by-step guide on how to do it:
- Identify the slope: This will be given to you. Let’s say the slope is m.
- Identify the point: You will also have a point, which we can denote as (x1, y1). For example, let’s say the point is (3, 4).
- Substitute the values into the slope-intercept equation: Since you have the slope and a point, you can substitute these values into the equation. The general form looks like this:
y = mx + b
Where y is the y-coordinate from your point, x is the x-coordinate from your point, and b is the y-intercept which you need to find. - Plug in the known values: Using our example, substitute the slope and the coordinates of the point into the equation.
4 = m(3) + b - Solve for b: Rearranging the equation allows you to solve for the y-intercept (b).
For instance, if the slope is 2, you would have
4 = 2(3) + b
which simplifies to
4 = 6 + b
Now, isolate b:
b = 4 – 6
b = -2 - Write the final equation: Now that you have the values of m and b, you can write the equation in slope-intercept form:
y = 2x – 2
In summary, given a slope and a point, plug them into the slope-intercept form to find the equation of the line easily. Just remember: y = mx + b where m is your slope and b is your y-intercept that you solved for!