how do u find the slope-intercept the y-intercept and the x-intercept
solve the equation for y
it will be in the form ... y = m x + b
... the x-coefficient (m) is the slope
... the constant term (b) is the y-intercept
set y equal to zero, and solve for x ... this is the x-intercept
If you have the intercepts at (a,0) and (0,b) then you can start off with the intercept form, which is
x/a + y/b = 1
Now just clear the fractions, and rearrange:
bx + ay = ab
y = -b/a x + b
To find the slope-intercept form of a linear equation, the y-intercept, and the x-intercept, you need the equation of the line in either the standard form (Ax + By = C) or the point-slope form (y - y1 = m(x - x1)).
1. Slope-Intercept Form (y = mx + b):
The slope-intercept form of a linear equation is y = mx + b, where:
- m represents the slope of the line.
- b represents the y-intercept, which is the point where the line intersects the y-axis.
To find the slope (m), you can compare the equation in either standard form or point-slope form and identify the coefficient of x. For example, if you have the equation y = 2x + 3, the slope (m) is 2.
To find the y-intercept (b), you can examine the equation and identify the constant term. In the same example, the y-intercept (b) is 3.
2. Y-Intercept:
The y-intercept is the value of y when the line intersects the y-axis (x = 0).
To find the y-intercept of an equation in standard form (Ax + By = C), you can set x = 0 and solve for y.
For example, if you have the equation 3x + 2y = 6, substitute x = 0 into the equation:
3(0) + 2y = 6
2y = 6
y = 3
Therefore, the y-intercept is 3.
3. X-Intercept:
The x-intercept is the value of x when the line intersects the x-axis (y = 0).
To find the x-intercept, you can set y = 0 in either the standard form or point-slope form and solve for x.
For example, if you have the equation y = -2x + 4 (in slope-intercept form), substitute y = 0 into the equation:
0 = -2x + 4
2x = 4
x = 2
Therefore, the x-intercept is 2.
In summary, to find the slope-intercept form, slope, y-intercept, and x-intercept:
- For slope-intercept form (y = mx + b): Identify the slope (m) and the y-intercept (b).
- For y-intercept: Set x = 0 in the equation and solve for y.
- For x-intercept: Set y = 0 in the equation and solve for x.