write the equation of each line in slope-intercept form. then graph the line?
Question:through (5,-2)with slope 2/3
recall the form,
y - y1 = m(x - x1)
where
m = slope
(x1 , y1) = point on the line
substituting,
y - (-2) = (2/3)*(x - 5)
y + 2 = (2/3)x - 10/3
y = (2/3)x - 10/3 - 2
y = (2/3)x - 10/3 - 6/3
y = (2/3)x - 16/3
*the slope-intercept form is in the form y = mx + b.
hope this helps~ :)
To write the equation of a line in slope-intercept form, we need two pieces of information: the slope (m) of the line and the y-intercept (b).
Given that the line passes through the point (5,-2) and has a slope of 2/3, we can use this information to find the equation.
Step 1: Find the y-intercept (b):
To find the y-intercept, we can substitute the coordinates of the given point (5,-2) into the slope-intercept form equation (y = mx + b), and solve for b.
-2 = 2/3 * 5 + b
-2 = 10/3 + b
To isolate b, we subtract 10/3 from both sides:
-2 - 10/3 = b
-6/3 - 10/3 = b
-16/3 = b
So, the y-intercept (b) is -16/3.
Step 2: Write the final equation:
Now that we have the slope (2/3) and the y-intercept (-16/3), we can write the equation in slope-intercept form:
y = mx + b
y = 2/3x - 16/3
To graph the line, you can follow these steps:
1. Plot the y-intercept, which is -16/3. This means that the line crosses the y-axis at the point (0, -16/3).
2. Use the slope (2/3) to find other points on the line. Since the slope is 2/3, it means that for every increase of 3 units in the x-direction, there is a corresponding increase of 2 units in the y-direction (rise over run). Start from the y-intercept and use this pattern to find other points. For example, from the y-intercept (0,-16/3), move 3 units to the right (increasing the x-value), and then move 2 units upward (increasing the y-value). This gives you the point (3, -10/3). You can continue this pattern to find other points.
3. Connect the points with a straight line.