Question

The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = one-half EndFraction(x – 1). What is the slope-intercept form of the equation for this line?

Answer 1

It's pretty simple. All you have to do is add 3 to both sides to get slope-intercept form after multiplying out the x/2-1/2. Just convert the 3 to 6/2 and add it over to get y=x/2+5/6. Slope intercept form just means to get a linear function in the form of y=mx+b, where mx is the slope of the linear function and b being the y intercept of the function. In this case, the y-intercept of the function is 5/6.

Answer 2

Before finding the slope intercept form of a line equation, we have to know that what is the slope-intercept form of a line. The slope-intercept form of a line is:
y = mx + c
Where:
m is the slope of the line and c is the y-intercept. y-intercept means how much a line cut the y-axis.
Now:
The given evaluation is:
\[(y - 3) = \frac{1}{2} (x -1) \]
\[\Rightarrow (y -3) = \frac{x}{2} - \frac{1}{2} \]
To get our required form, we have to add 3 to the both side of the previous equation.
Adding 3 to the both side of the previous equation, we have:
\[y - 3 + 3 = \frac{x}{2} - \frac{1}{2} + 3 \]
\[\Rightarrow y = \frac{x}{2} + \frac{5}{2} \]
This is the required form of our equation.