Question

[20 Points] I need help with these questions:

I will give brainliest to best answer!

1) Write the equation in slope-intercept form that contains the following point and is perpendicular to the given line

y = -4x + 3; (4, -2)


2) Write the equation in slope-intercept form that contains the following two points.

(4, -1) (-2, 8)


3) Given the equation y = 3x + 5 , write the equation of a new line that would have the same y-intercept but would be steeper.

Answer 1

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

You need to find "m" and "b"

1.) For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -2/3

perpendicular line's slope is 3/2

The given line's slope is -4, so the perpendicular line's slope is 1/4.

y = 1/4x + b

To find "b", you can plug in the point (4, -2) into the equation

y = 1/4x + b

-2 = 1/4(4) + b

-2 = 1 + b

-3 = b

$y=\frac{1}{4} x-3$

2.) To find "m", use the slope formula and plug in the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{8-(-1)}{-2-4}$

$m=\frac{8+1}{-2-4}$

$m=\frac{9}{-6} =-\frac{3}{2}$

y = -3/2x + b

Plug in one of the points to find "b"

y = -3/2x + b

-1 = -3/2(4) + b

-1 = -6 + b

5 = b

$y=-\frac{3}{2}x +5$

3.) y-intercept: 5 (since the given equation's y-intercept is 5)

I'm confused with what they mean by "steep", so I'll try to update this later unless someone else has an answer

So I looked it up, and it says that a steep slope is a line that is more vertical [if that makes sense]. So you could do a slope of +3 (more than 3, like 4, 5, 6...) because the given line's slope is 3, and you need a new line that is more steeper(vertical)