Question

Write an equation of the line in slope-intercept form that passes through the point (-6, 1) and has a slope of ½.

Answer 1

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 2

Answer:

$y = \frac{1}{2} x + 4$

Step-by-step explanation:

Slope intercept form is:

$y = mx +b$

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:

$y - y_{1} = m (x - x_{1} )$

We are given that the slope is $\frac{1}{2}$, so we plug it in for m:

$y - y_1 = \frac{1}{2} (x-x_1)$

Now, we need to plug in the given value of $x_1$ and $y_1$ in the point (-6, 1), where the x = -6 and y = 1. So it will look like this when plugged into the equation:

$y - 1 = \frac{1}{2} (x-(-6))$

Solve for y (isolate y on one side):

$y - 1 = \frac{1}{2} (x-(-6))\\\\y - 1 = \frac{1}{2} (x+6)\\\\y - 1 = \frac{1}{2} x+3\\\\\\y= \frac{1}{2}x+4$

Final answer is: y = 1/2x + 4