-and-(-3-1)-in-slope-intercept-form.jpeg "(-1 3) And (-3 1) In Slope Intercept Form")
Converting (-1, 3) and (-3, 1) to Slope-Intercept Form
In this article, we will explore how to convert two points, (-1, 3) and (-3, 1), into slope-intercept form.
What is Slope-Intercept Form?
The slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where:
- m is the slope of the line (a measure of how steep it is)
- b is the y-intercept (the point at which the line crosses the y-axis)
Point 1: (-1, 3)
To convert the point (-1, 3) into slope-intercept form, we need to find the slope (m) and the y-intercept (b).
Step 1: Find the Slope (m)
To find the slope, we need another point on the line. Let's use the point (-3, 1) as our second point.
The slope (m) is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-1, 3) and (x2, y2) = (-3, 1)
m = (1 - 3) / (-3 - (-1)) m = (-2) / (-2) m = 1
Step 2: Find the Y-Intercept (b)
Now that we have the slope, we can use one of the points to find the y-intercept. We'll use the point (-1, 3).
The equation for the slope-intercept form is:
y = mx + b
Substitute the values:
3 = 1(-1) + b 3 = -1 + b b = 4
Slope-Intercept Form for Point (-1, 3)
Now that we have the slope (m) and y-intercept (b), we can write the equation in slope-intercept form:
y = x + 4
Point 2: (-3, 1)
Let's repeat the process for the point (-3, 1).
Step 1: Find the Slope (m)
We already found the slope in the previous example: m = 1.
Step 2: Find the Y-Intercept (b)
Use the point (-3, 1) to find the y-intercept:
1 = 1(-3) + b 1 = -3 + b b = 4
Slope-Intercept Form for Point (-3, 1)
The equation in slope-intercept form is:
y = x + 4
Conclusion
Both points, (-1, 3) and (-3, 1), have the same equation in slope-intercept form: y = x + 4. This means that they both lie on the same line.
