Answer:
y = 1/2x +4
Step-by-step explanation:
You are given the slope (m) of the line and a point, and asked for slope-intercept form:
y = mx +b . . . . . . . line with slope m and y-intercept b
The value of the intercept, b, can be found from the point by rearranging this equation to ...
b = y -mx
b = 1 -1/2(-6) = 4 . . . . using x=-6, y=1
Then the equation of the line with m=1/2 and b=4 is ...
y = 1/2x +4
Answer:
[tex]y = \frac{1}{2} x + 4[/tex]
Step-by-step explanation:
Slope intercept form is:
[tex]y = mx +b[/tex]
y and x remain as variables and don't get changed or touched.
m is the slope of the line.
b is the y-intercept of the line.
To find the information needed for this form, we need to use the equation:
[tex]y - y_{1} = m (x - x_{1} )[/tex]
We are given that the slope is [tex]\frac{1}{2}[/tex], so we plug it in for m:
[tex]y - y_1 = \frac{1}{2} (x-x_1)[/tex]
Now, we need to plug in the given value of [tex]x_1[/tex] and [tex]y_1[/tex] in the point (-6, 1), where the x = -6 and y = 1. So it will look like this when plugged into the equation:
[tex]y - 1 = \frac{1}{2} (x-(-6))[/tex]
Solve for y (isolate y on one side):
[tex]y - 1 = \frac{1}{2} (x-(-6))\\\\y - 1 = \frac{1}{2} (x+6)\\\\y - 1 = \frac{1}{2} x+3\\\\\\y= \frac{1}{2}x+4[/tex]
Final answer is: y = 1/2x + 4
