Question

lse the given conditions to write an equation for the line in the indicated form. Passing through (2,-3) and paratiel to the line whose equation is y=-8x+2 slope-intercept form

Answer 1

Answer: y = -8x + 13

Explanation:

Our task is to write the equation of the line, given that the new line:

• passes through (2,-3)
• is parallel to y = -8x + 2

Since the new line and y = -8x + 2 are parallel, their slopes are equal. Therefore, the slope of the new line is -8.

Now, we know both a point and the slope of the line, so we write it in point-slope form:

`y-y_1=m(x-x_1)`

Plug in the data:

`y-(-3)=-8(x-2)`

`y+3=-8(x-2)`

`y+3=-8x+16`

`y=-8x+13`

Therefore, the equation is y = -8x + 13.

Answer 2

Explanation:

Since the line we are looking for is parallel to the line with equation y = -8x + 2, it will have the same slope. The slope of the given line is -8.

Using the point-slope form of a linear equation, we can write the equation of the line passing through (2,-3) with a slope of -8:

y - y1 = m(x - x1)

where (x1, y1) = (2, -3) and m = -8.

Plugging in these values, we have:

y - (-3) = -8(x - 2)

Simplifying, we get:

y + 3 = -8x + 16

Subtracting 3 from both sides, we have:

y = -8x + 13

So the equation of the line passing through (2,-3) and parallel to y = -8x + 2 in slope-intercept form is y = -8x + 13.