How do I use an x and y-intercept to write an equation in standard form? For example, how do I use the x-intercept of 3 and y-intercept of 6 to write an equation in standard form?
The x-intercept of 3 is really the point (3,0) and
the y-intercept of 6 is really the point (0,6)
So you are just given two points,
find the slope, then find the equation of the line in your usual way.
Okay, but how can I (if I can) write an equation in standard form (ax + by = c) using the two intercepts?
Ahh, you mean directly?
x/3 + y/6 = 1
(in general: x/(x-intercept) + y/(y-intercept) = 1 )
once you have that, multiply each term by 6, the LCD
2x + y = 6
check if both points lie on it.
for (3,0)
2(3) + 0 = 6 , ok
for (0,6)
0 + 6 = 6 , ok
Thank you so much! It is surprising that my school didn't show us that method.
To write an equation in standard form using the x-intercept and y-intercept, you need to follow a few steps:
1. Understand the concept of intercepts: The x-intercept is the value of x when the line intersects the x-axis (y = 0), and the y-intercept is the value of y when the line intersects the y-axis (x = 0).
2. Use the intercept values: In this case, the x-intercept is 3 and the y-intercept is 6.
3. Write the equation in slope-intercept form: The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
4. Find the slope: To find the slope (m), you can use the formula: m = (change in y) / (change in x). Since we have the y-intercept at (0, 6) and the x-intercept at (3, 0), we can calculate the slope as (0 - 6) / (3 - 0) = -6/3 = -2.
5. Substitute the slope and y-intercept into the slope-intercept form: Using the slope-intercept form y = mx + b, substitute the slope (-2) and y-intercept (6) to get y = -2x + 6.
6. Rewrite the equation in standard form: Standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive. To write the equation in standard form, move all terms to the same side of the equation, so the equation becomes 2x + y = 6.
So, the equation in standard form using the x-intercept of 3 and y-intercept of 6 is 2x + y = 6.