Question

Write equation for the line in slope intercept form (6,4) and (3,8)

Answer 1

To find the equation of the line passing through (6,4) and (3,8), calculate the slope using the two points, then use one of the points to write the point-slope form and convert it to slope-intercept form, resulting in y = (-4/3)x + 12.

Step-by-step explanation:

To find the equation of the line in slope-intercept form, we first need to calculate the slope (m) using the two points given, which are (6,4) and (3,8). The formula to calculate the slope is:

m = (y2 - y1) / (x2 - x1)

Plugging in the values from the two points, we get:

m = (8 - 4) / (3 - 6)

m = 4 / -3

m = -4/3

Now that we have the slope, we can use the point-slope form to create the equation of the line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line. We can use the point (6, 4):

y - 4 = (-4/3)(x - 6)

Then we solve for y to get the slope-intercept form, y = mx + b:

y - 4 = (-4/3)x + 8

y = (-4/3)x + 8 + 4

y = (-4/3)x + 12

So, the equation of the line in slope-intercept form using the points (6,4) and (3,8) is y = (-4/3)x + 12.

Answer 2

Answer: y = - 4x/3 + 12

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

m represents the slope of the line.

m = (y2 - y1)/(x2 - x1)

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (6, 4) and (3, 8),

y2 = 8

y1 = 4

x2 = 3

x1 = 6

Slope,m = (8 - 4)/(3 - 6) = 4/- 3 = - 4/3

To determine the y intercept, we would substitute x = 3, y = 8 and m= - 4/3 into y = mx + c. It becomes

8 = - 4/3 × 3 + c

8 = - 4 + c

c = 8 + 4

c = 12

The equation becomes

y = - 4x/3 + 12