To write the equation of a line in slope-intercept form, we need to determine the slope of the line and the y-intercept.
The slope-intercept form of the equation of a line is given by:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
To find the equation of a line in slope-intercept form, we need to determine the values of m and b.
Here are two examples:
The line passes through the points (2, 4) and (4, 8).
To find the slope, we use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (2, 4) and (x2, y2) = (4, 8)
m = (8 - 4)/(4 - 2) = 2
To find the y-intercept, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is one of the points on the line, for example, (2, 4).
y - 4 = 2(x - 2)
y - 4 = 2x - 4
y = 2x + 0
Therefore, the equation of the line in slope-intercept form is y = 2x.
The line passes through the point (3, 7) and has a slope of -3.
We can use the point-slope form of the equation of a line to find the equation in slope-intercept form.
y - y1 = m(x - x1)
where (x1, y1) is the given point, (3, 7), and m is the slope, which is -3.
y - 7 = -3(x - 3)
y - 7 = -3x + 9
y = -3x + 16
Therefore, the equation of the line in slope-intercept form is y = -3x + 16