Question

when writing the equation of a line in slope-intercept form, how can you determine the value of m in y=mx+b if you know the coordinates of two points on the line?

Answer 1

Answer:

y = -2.5 x + 6.5

Step-by-step explanation:

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