writing an equation of the line in slope intercept form

Question

writing an equation of the line in slope- intercept form. (theirs two questions)

1.) the line passes through (-1,3) and (-4,5)

2.) The line with slope -2.5 and passing through (2,1.5)

Thank you so much!

Answer 1

The equation of a line in slope-intercept form is written as

y = mx + b where m is the slope and b is the y-intercept.

a) We can find the slope of the line passing through (-1,30 and (-4, 5) by subtracting the y coordinates and dividing the difference by the difference if the x coordinates:

m = (5 - 3 ) = 2

-4 - (-1) -3

Now use this slope and substitute the coordinates of either of the given points to find the y-intercept, b . Let's use (-1,3):

y = mx + b

3 = -2 • -1 + b

3

3= 2 + b

3

7 = b

3

The equation of the line will be y = -2 x + 7

3 3

b) Using y = mx + b, we can substitute -2.5 for the slope and use the point to find the y-intercept:

y = -2.5x + b

1.5 = -2.5 • 2 + b

1.5 = -5 + b

6.5 = b

The equation of the line will be:

y = -2.5 x + 6.5

Answer 2

The equation of a line in slope-intercept form is written as

y = mx + b where m is the slope and b is the y-intercept.

a) We can find the slope of the line passing through (-1,30 and (-4, 5) by subtracting the y coordinates and dividing the difference by the difference if the x coordinates:

m = (5 - 3 ) = 2

-4 - (-1) -3

Now use this slope and substitute the coordinates of either of the given points to find the y-intercept, b . Let's use (-1,3):

y = mx + b

3 = -2 • -1 + b

3

3= 2 + b

3

7 = b

3

The equation of the line will be y = -2 x + 7

3 3

b) Using y = mx + b, we can substitute -2.5 for the slope and use the point to find the y-intercept:

y = -2.5x + b

1.5 = -2.5 • 2 + b

1.5 = -5 + b

6.5 = b

The equation of the line will be:

y = -2.5 x + 6.5

Answer 3

I will show you how to work the first problem, then you try the second problem. Get the slope m.

m = (y₂ - y₁) / (x₂ - x₁)

x₁ = -1

y₁ = 3

x₂ = -4

y₂ = 5

Plug in the numbers and get m.

y = mx + b

Plug your result for m into this equation, and plug in the coordinates of either given point to solve for b:

y₁ = mx₁ + b

You can also find b from

y₂ = mx₂ + b

For the second problem, you already have the slope,

Answer 4

Slope-intercept form is y=mx+b where m is the slope and b is the intercept.

1. To find the slope, use this equation y2-y1 over x2-x1 so we plug in those values into the equation

(5-3)/(-4 - -1) = (5-3)/(-4+1) = 2/-3 so we have the slope. To find the intercept, simply plug in one of the passing points into the equation y= -2/3x+b

3=-2/3(-1)+b -> 3=2/3+b -> 3-2/3=b -> 7/3=b

So the equation is

y=-2/3x+7/3 (simplify how you wish)

For the second problem, we already have the slope, so we don't need to do what we did in the previous problem. We have y=-2.5x+b - plug in those numbers to find the intercept!

1.5=-2.5(2)+b -> 1.5=-5+b -> 1.5+5=b -> 6.5=b

So you have the equation y=-2.5x+6.5 (please don't miss any negatives!)