Question

I need serious help please!

Equation of a line: given that m equals 5 and P(2,3), find the y-intercept (b), and write the equation of the line in slope intercept form

Equation of a line: given that m equals -2 and P(-4,5), find the y-intercept (b), and right equation of the line and slope intercept form

Giving P(3, -5) and Q(6,3). Find the slope of the line passing through the two points

Answer 1

1. y-intercept = -7

equation: y = 5x - 7

2. y-intercept = -3

equation: y = -2x - 3

3. slope =
`(8)/(3)`

Explanation:

slope-intercept form: y = mx + b

slope formula:
`(y2 - y1)/(x2 - x1)`

To write an equation in slope-intercept form, you need to know the slope(m) and the y-intercept(b).

1. Given: m = 5, P(2, 3). To find the y-intercept, input the given values of m and the point into the equation format and solve for b:

y = mx + b

3 = 5(2) + b

3 = 10 + b

-7 = b

The y-intercept is -7.

Now that we know the slope and the y-intercept, we can write the equation:

y = 5x - 7

2. Given: m = -2, P(-4, 5). To find the y-intercept, input the given values of m and the point into the equation and solve for b:

y = mx + b

5 = -2(-4) + b

5 = 8 + b

-3 = b

The y-intercept is -3.

Now that we know the slope and the y-intercept, we can write the equation:

y = -2x - 3

3. Given: P(3, -5), Q(6, 3). To find the slope, input the given points into the slope formula:

(3, -5) = (x1, y1)

(6, 3) = (x2, y2)

`(y2-y1)/(x2-x1)`

`(3-(-5))/(6-3)`

Simplify:

3 - (-5) = 3 + 5 = 8

6 - 3 = 3

`(8)/(3)`

The slope of the line passing through points P and Q is
`(8)/(3)`.

I hope this helps. :)