Question

Line a passes through points (-2, 1) and (2, 9). Write an equation in slope intercept form that is parallel to line a. Show your work Provid the correct slope, write an equation, provid the equation of the line in the problem and equation of a line parallel

Answer 1

y = 2x + 1

Explanation:

To find the slope of a line passing through two points, we can use the following formula:

`\sf Slope(m) = (y_2 - y_1)/(x_2 - x_1)`

Where (x1, y1) and (x2, y2) are the two points.

In this case, we have:

`\sf Slope = (9 - 1)/(2 - (-2))= (8 )/( 4 )= 2`

Therefore, the slope of line a is 2.

Since parallel lines have the same slope, the equation of the line parallel to line a will also have a slope of 2.

To write the equation of the line in slope-intercept form, we can use the following formula:

y = mx + b

Where m is the slope of the line and b is the y-intercept.

Since we know that the slope of the line is 2, we can substitute that value into the equation:

y = 2x + b

To solve for b, we can use one of the two points that line a passes through. Let's use the point (-2, 1):

1 = 2(-2) + b

1 = -4 + b

1 + 4 = b

5 = b

b = 5

Therefore, the equation of the line a is:

y = 2x + 5

Equation of the line parallel to the line a is:

y = 2x + 1

Note:

There are lots of parallel lines, which constant terms only varies.