find the slope-intercept form for the line satisfying the following conditions: x-intercept 3, y-intercept 2/3
y = m x + b
when y= 0, x = 3
when x = 0, y = 2/3
so
2/3 = 0 + b or b = 2/3
y = m x + 2/3
then
when y = 0 , x = 3
0 = m (3) + 2/3
m = - 2/9
so
y = -2/9 x + 2/3
or
9 y = -2 x + 6
To find the slope-intercept form of a line, you need two pieces of information: the slope of the line (denoted as "m") and the y-intercept (denoted as "b").
Given that the x-intercept is 3 and the y-intercept is 2/3, let's find the values of m and b.
The x-intercept occurs when y = 0, and it tells us the specific x-coordinate where the line crosses the x-axis. In this case, the x-intercept is 3. Therefore, one point on the line is (3, 0).
The y-intercept occurs when x = 0, and it tells us the specific y-coordinate where the line crosses the y-axis. In this case, the y-intercept is 2/3. Therefore, another point on the line is (0, 2/3).
To find the slope (m), we utilize the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Plugging in the coordinates (3, 0) and (0, 2/3), we get:
m = (0 - 2/3) / (3 - 0) = -2/9.
Now that we know m = -2/9, we can rewrite the equation of the line in slope-intercept form, y = mx + b, where b is the y-intercept.
Using the point (0, 2/3), we can substitute the values into the equation:
2/3 = (-2/9)(0) + b.
This simplifies to:
2/3 = b.
Therefore, the y-intercept is b = 2/3.
Finally, plugging in m = -2/9 and b = 2/3 into the slope-intercept form, we have:
y = (-2/9)x + 2/3.
Hence, the slope-intercept form of the line is y = (-2/9)x + 2/3.