Find slope of line, two points on the line are included

In summary, the conversation was about finding the slope of a line that passes through two given points (-16, -1) and (-17, -7). The equation y = mx + b was used, and the correct gradient was found to be 6. The individual also learned about the point-slope formula y-y0 = m(x-x0) and used it to find the y-intercept b = 95.
  • #1
rcmango
234
0

Homework Statement



find the slope of this line it contains these points:

(-16, -1) , (-17, -7)

Homework Equations



y = mx + b

The Attempt at a Solution



i got y = 3/8x - .625

is that correct?

my work i use -7 +1 / -17 + 1

==-6/16


==6/16 = 3/8

then i used -7 = 3/8 * -17 + b

=6.375
 
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  • #2
rcmango said:

Homework Statement



find the slope of this line it contains these points:

(-16, -1) , (-17, -7)

Homework Equations



y = mx + b

The Attempt at a Solution



i got y = 3/8x - .625

is that correct?

my work i use -7 +1 / -17 + 1

==-6/16


==6/16 = 3/8

then i used -7 = 3/8 * -17 + b

=6.375

Not quite, you got the gradient wrong. In the formula

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

You mistakenly substituted y1 a second time where x1 is instead meant to be.

Also, your technique to find the missing value of b works, but you might also be interested to know that there is a formula for a line that has gradient m and passes through the point (x0,y0) as

[tex]y-y_0=m(x-x_0)[/tex]

And if we divide both sides by x-x0, you may see it is quite similar to the gradient formula:

[tex]m=\frac{y-y_0}{x-x_0}[/tex]
 
  • #3
thankyou upon checking my work, i got the m = 6

and the b = 95

and I also used the new point slope formula, thanks.
 

1. What is the formula for finding the slope of a line?

The slope of a line is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

2. How do I find the slope of a line given two points?

To find the slope of a line, you need to know the coordinates of two points on the line. Then, use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.

3. Can I find the slope of a line if I only have one point?

No, you need at least two points to calculate the slope of a line. If you only have one point, the slope cannot be determined.

4. How do I interpret the slope of a line?

The slope of a line represents the rate of change between two variables. A positive slope indicates that the line is increasing, while a negative slope indicates a decreasing line. A slope of zero indicates a horizontal line, and a slope of infinity indicates a vertical line.

5. Can the slope of a line be negative?

Yes, the slope of a line can be negative. A negative slope indicates that the line is decreasing as the x-coordinate increases. This means that there is a negative correlation between the two variables represented by the x and y coordinates.

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