How can I find y-intercept when given the slope and a point
y = m x + b
y intercept is when x = 0 so we need to find b
given (xi , yi) and m
yi = m xi + b
so
b = yi - m xi
(we know yi, m and xi so we have it)
thank you
To find the y-intercept when given the slope and a point, you can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where:
- (x1, y1) represents the given point.
- m represents the slope of the line.
To find the y-intercept, you need to replace x and y in the equation with the coordinates of the given point (x1, y1). Then, solve the equation for y.
1. Start by substituting the values of the point (x1, y1) and the slope (m) into the point-slope form of the linear equation.
y - y1 = m(x - x1)
2. Simplify the equation by distributing the slope to the x terms.
y - y1 = m*x - m*x1
3. Move the term containing y to one side of the equation by adding y1 to both sides.
y = m*x - m*x1 + y1
4. Now, you have the equation in the slope-intercept form (y = mx + b), where b represents the y-intercept. The value of b can be found by comparing the equation to the slope-intercept form.
Comparing both forms, you can see that b = -m*x1 + y1.
Therefore, the y-intercept is -m*x1 + y1.