-and-(-3-3)-in-slope-intercept-form.jpeg "(-9 5) And (-3 3) In Slope Intercept Form")
Writing Equations in Slope-Intercept Form: (-9, 5) and (-3, 3)
In this article, we will explore how to write the equations of two lines in slope-intercept form, given their points: (-9, 5) and (-3, 3).
What is Slope-Intercept Form?
The slope-intercept form of a linear equation is a way of writing the equation of a line in the form:
y = mx + b
where:
- m is the slope of the line (a measure of how steep it is)
- b is the y-intercept of the line (the point where the line crosses the y-axis)
Finding the Equation of the Line Passing Through (-9, 5)
To find the equation of the line passing through the point (-9, 5), we need to find the slope (m) and the y-intercept (b).
Let's use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope.
We can plug in the point (-9, 5) into the equation:
y - 5 = m(x - (-9))
y - 5 = m(x + 9)
Now, we need to find the slope (m). Let's assume we know the slope is m. We can then rewrite the equation in slope-intercept form:
y = mx + b
To find b, we can plug in the point (-9, 5) into the equation:
5 = m(-9) + b
Simplifying the equation, we get:
b = 5 + 9m
So, the equation of the line passing through (-9, 5) in slope-intercept form is:
y = mx + (5 + 9m)
Finding the Equation of the Line Passing Through (-3, 3)
Using the same process, we can find the equation of the line passing through the point (-3, 3).
y - 3 = m(x - (-3))
y - 3 = m(x + 3)
Assuming the slope is m, we can rewrite the equation in slope-intercept form:
y = mx + b
To find b, we can plug in the point (-3, 3) into the equation:
3 = m(-3) + b
Simplifying the equation, we get:
b = 3 + 3m
So, the equation of the line passing through (-3, 3) in slope-intercept form is:
y = mx + (3 + 3m)
Conclusion
In this article, we learned how to write the equations of two lines in slope-intercept form, given their points: (-9, 5) and (-3, 3). We used the point-slope form of a linear equation to find the slope and y-intercept of each line, and then rewrote the equations in slope-intercept form.
