Write an equation in slope-intercept form of the line that passes through (−5, 19) and (5, 13)

Answer 1

Hello, P S.,

Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept (where the line passes through the y axis at x = 0).

The slope is defined as the rise over the run (rise/run) of the equation. It literally means that if you take the two points provided, you can calculate the "run," which is the distance travelled along the x axis from left to right. For (-5, 19) and (5, 13), the run would be 5 + 5 = 10 (you need the absolute value of -5 to get the distance). Another way to do this is to take the right hand value (5) and subtract the starting value (-5) to arrive at the same answer, 10. That is the "run." The rise is how much the y value changes over the same change in x. Here, we take the (5, 13) and subtract the 19 from the 13, to get -6 for the rise. (A minus means it drops as x increases). So the slope is -6/10, or -0.6.

We can put that into the equation to make it y = -0.6x + b.

We need to find b, so let's put in the values of x and y of the provided points the line crosses. Since these points satisfy the line equation, we can use them to calculate b.

For (-5, 19), we get: 19 = -0.6*(-5) + b

19 = 3 + b, b = 16

This would mean y = -0.6x + 16 is the line we are seeking.

To double check, use the other data set of (5, 13) and see if it works:

13 = -0.6(5) + 16 ??? 13 = -3 + 16; 16 = 16: YES

y = -0.6x + 16, with points (-5, 19) and (5, 13) noted. (Each chart line is 2.)

Bob

Answer 2

Hello P.S,

First you have to know the equation of a straight line in slope intercept form is : y = mx + b ,

where m is the slope of the line , and b is the y-intercept of the line.

Now given two points , we have to find out the slope m of the line using formula, where (x₁,y₁) and ( x₂, y₂₎) are the points (-5, 19) and ( 5, 13) respectively.

so, m =( y₂- y₁)/ ( x₂-x₁)

substituting the values, m= (13 -19)/ ( 5 + 5 ) , (here x₁ = -5)

m= - 6 / 10 = -3/5

slope of the line is -3 / 5

now we consider the formula of equation of the line in point slope form which is

( y - y₁ ) = m ( x - x₁ ) here we consider one point from the problem that is ( - 5 , 19 ) ...... substituting the value of m and the co-ordinates of one point we get,

(y - 19 ) = - 3/5 ( x + 5 ) ( here x₁ is - 5 )

now lets calculate , multiplying by 5 both sides we get,

5 ( y - 19 ) = - 3 ( x + 5 )

eliminating brackets from both sides we get,

5y - 95 = -3x - 15

adding 95 on both sides, 5y = -3x -15 + 95

5y = -3x + 80

dividing by 5 both sides, y = - 3/5 x + 16

now we have slope intercept form ANS..

Answer 3

Hi P. S.

You have the coordinates of two points. (5,13) and (-5,19)

Use those to calculate the slope, m where m = (y₂ - y₁)/(x₂ - x₁)

Then use one set of your given points to solve for b in y = mx + b

m = (13 - 19)/(5 -(-5)) = -6/10 = -3/5

y = (-3/5)x + b

13 = (-3/5)5 + b

13 = -3 + b

13 + 3 = b

16 = b

y = (-3/5)x + 16

You can graph your line at Desmos.com see it that it passes through the given points