Write the equation in slope-intercept form of the line that passes through (10,7) and (-2,-9)

Answer 1

Hi...

Remember the slope-intercept form of a line is y = mx + b

Whenever you are given TWO points (on a line) and nothing else, use the two points to calculate the slope, m and the point-slope formula.

Taking p1 (10, 7) and p2 (-2, -9), calculate the slope as the change in y over the change in x.

Remember that it does not matter which point you make p1 and p2, the slope will be the same.

m = (y2 - y1)/(x2 - x1) = (-9 - 7)/(-2 - 10) = -16 / -12 = ⁴/₃

Now use the point-slope formula, the calculate value of m and one of the points for (x1, y1)

y - y1 = m (x - x1) - Point Slope Formula

y - 7 = ⁴/₃( x - 10)

y - 7 = ⁴/₃( x ) -⁴/₃(10)

y - 7 = ⁴/₃( x ) - ⁴⁰/₃

_{y =} ⁴/₃( x ) - ⁴⁰/₃ + 7.....Solve -⁴⁰/₃ + 7 = (-40 + 21)/3 = -¹⁹/₃

_{y =} ⁴/₃( x ) - ¹⁹/₃ Final Answer

Hope this helps...

Answer 2

Slope intercept form is defined as y=mx+b where m is the slope of the differences between your y coordinates over your x coordinates, b is the y-intercept or the y value when x is equal to 0 and x,y are coordinate variables in your line.

So coordinates are written in the form (x,y) therefore your 1st coordinate ( 10,7) has a x value =10 and a y value = 7. Other coordinate, (-2,-9) has an x coordinate of -2 and a y coordinate of -9.

m is the slope, which is the difference of y coordinates over x coordinates. Therefore, y2-y1/(x2-x1)

1 and 2 are your first and second coordinate of y or x respectively. Substitute or replace your coordinates given in the problem. The result would be

-9-7/(-2-10)=-16/-12=16/12=4/3( simplified)

Therefore the slope is 4/3.

To find the y intercept, substitute your slope m, with a coordinate to y=mx+b

Result with your first coordinate (10,7) is

7=(4/3)*10+b

then rearrange so b is alone on one side so, you can minus b on both sides, then minus 7 on both sides, resulting in

-b=(4/3)*10-7

Times the full equation by -1 to get rid of the negative sign on b, leading to

b=-(4/3)*10+7

b=(-40/3)+7

b=(-40/3)+21/3=-19/3

OR

b=-13.3333+7

b=-6.33333

Your answer therefore is y=(4/3)x+(-19/3)

Answer 3

You are asked to find the equation of the line that passes through 2 points: (10,7) and (-2,-9).

1st step: Find the slope of the line

slope: m = change in y / change in x

m = (7-(-9)) / (10-(-2))

m = (7+9) / (10+2)

m = 16 / 12

m = 4 / 3

2nd step: Put one of the given points and the slope into the "Point-Slop formula": y - y₁ = m (x - x₁) and simplify to obtain the equation in Slope-Intercept Form

y - 7 = 4/3 (x -10)

y - 7 = 4/3x - 40/3

y = 4/3x - 40/3 + 7

y = 4/3x - 19/3

Equation of the line that passes through (10,7) and (-2,-9) in Slope-Intercept Form: y = 4/3x - 19/3

Note: "Slope-Intercept Form" means that the equation is denoting the Slope (m) and the y-intercept (b):

y = mx + b