Question

On a coordinate plane, a line goes through (negative 6, 8) and (2, 6). A point is at (negative 2, negative 4). What is the slope of the line that is parallel to the given line and passes through the given point? What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point? What is the y-intercept of the line that is parallel to the given line and passes through the given point?

Answer 1

Answer:

1. -1/4

2.  y + 4 = –1/4(x + 2)

3. -9/2

Step-by-step explanation:

Answer 2

Answer:

Part 1) The slope of the line that is parallel to the given line is $m=-\frac{1}{4}$

Part 2) The equation, in point-slope form, of the line that is parallel to the given line and passes through the given point is

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

Part 3) The y-intercept is the point (0,-4.5)

Step-by-step explanation:

Part 1) What is the slope of the line that is parallel to the given line and passes through the given point?

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(-6,8) and (2,6)

substitute

$m=\frac{6-8}{2+6}$

$m=-\frac{1}{4}$

step 2

Find the slope of the line that is parallel to the given line

we know that

If two lines are parallel, then their slopes are equal

so

The slope of the line that is parallel to the given line is also

$m=-\frac{1}{4}$

Part 2) What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?

we know that

The equation of the line in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{4}$

$point\ (-2,-4)$

substitute

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

Part 3) What is the y-intercept of the line that is parallel to the given line and passes through the given point?

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the linear equation

$y+4=-\frac{1}{4}(0+2)$

solve for y

$y+4=-0.5\\y=-4.5$

therefore

The y-intercept is the point (0,-4.5)