-%26amp%3B-(0-3)-in-slope-intercept-form.jpeg "(-4 5) & (0 3) In Slope Intercept Form")
Converting Point-Slope Form to Slope-Intercept Form: (-4, 5) and (0, 3)
In this article, we will explore how to convert point-slope form to slope-intercept form using two points: (-4, 5) and (0, 3).
What is Point-Slope Form?
Point-slope form is a way to express a linear equation using a single point on the line and the slope of the line. The general formula for point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
What is Slope-Intercept Form?
Slope-intercept form is another way to express a linear equation, and it is written in the form:
y = mx + b
where m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis).
Converting Point-Slope Form to Slope-Intercept Form
To convert point-slope form to slope-intercept form, we need to follow these steps:
- Determine the slope (m): We can find the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
- Determine the y-intercept (b): We can find the y-intercept by plugging the slope and one of the points into the slope-intercept form.
Let's apply these steps to our two points: (-4, 5) and (0, 3).
Example 1: Converting (-4, 5) to Slope-Intercept Form
To find the slope, we need another point on the line. Let's use the point (0, 3). Then, we can find the slope using the formula:
m = (3 - 5) / (0 - (-4)) = -2 / 4 = -1/2
Now, we can plug the slope and the point (-4, 5) into the slope-intercept form:
y = mx + b y = (-1/2)x + b
To find the y-intercept (b), we can plug in the point (-4, 5):
5 = (-1/2)(-4) + b 5 = 2 + b b = 3
So, the slope-intercept form of the line passing through (-4, 5) is:
y = (-1/2)x + 3
Example 2: Converting (0, 3) to Slope-Intercept Form
We can follow the same steps as before. Let's find the slope using the point (-4, 5):
m = (5 - 3) / (-4 - 0) = 2 / -4 = -1/2
Now, we can plug the slope and the point (0, 3) into the slope-intercept form:
y = mx + b y = (-1/2)x + b
To find the y-intercept (b), we can plug in the point (0, 3):
3 = (-1/2)(0) + b 3 = b
So, the slope-intercept form of the line passing through (0, 3) is also:
y = (-1/2)x + 3
As we can see, both points result in the same slope-intercept form, which means they lie on the same line.
Conclusion
In this article, we have learned how to convert point-slope form to slope-intercept form using two points: (-4, 5) and (0, 3). By following the steps, we can find the slope and y-intercept, and then write the equation in slope-intercept form.
