-(0-4)-in-slope-intercept-form.jpeg "(-3 0) (0 4) In Slope Intercept Form")
Converting (-3, 0) and (0, 4) to Slope-Intercept Form
In this article, we will explore how to convert two points, (-3, 0) and (0, 4), into the slope-intercept form of a linear equation.
What is Slope-Intercept Form?
The slope-intercept form of a linear equation is a way of expressing a line 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 where the line crosses the y-axis)
Finding the Slope (m)
To find the slope, we need to use the two points given: (-3, 0) and (0, 4). We can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-3, 0) and (x2, y2) = (0, 4).
m = (4 - 0) / (0 - (-3)) m = 4 / 3
So, the slope (m) is 4/3.
Finding the Y-Intercept (b)
Now that we have the slope, we can use one of the points to find the y-intercept (b). We can use the point (0, 4) and the slope (4/3) to find b.
y = mx + b 4 = (4/3)(0) + b 4 = b
So, the y-intercept (b) is 4.
The Slope-Intercept Form
Now that we have the slope (m) and the y-intercept (b), we can write the equation in slope-intercept form:
y = mx + b y = (4/3)x + 4
And that's it! We have successfully converted the two points (-3, 0) and (0, 4) into the slope-intercept form of a linear equation.
