Question

a line with a slope of 7/3 passes through points 4,-8 and d,-1 what is the value of d

Answer 1

To find the value of d, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is 7/3, we can substitute this into the equation to get:
y = (7/3)x + b

Next, we can substitute the given point (4, -8) into the equation to find the value of b.

-8 = (7/3)(4) + b

Multiply both sides by 3 to get rid of the fraction:
-24 = 28 + 3b

Subtract 28 from both sides:
-24 - 28 = 3b
-52 = 3b

Divide both sides by 3:
-52/3 = b

Now, we have the equation:
y = (7/3)x - 52/3

Finally, we can substitute the value of y as -1 (from the given point (d, -1)) into the equation to find the value of d.

-1 = (7/3)d - 52/3

Add 52/3 to both sides:
-1 + 52/3 = 7/3 * d

To add -1 and 52/3, we need to rewrite -1 as -3/3:
-3/3 + 52/3 = 7/3 * d

49/3 = 7/3 * d

Now, we can divide both sides by 7/3 to solve for d:
(49/3) / (7/3) = d

Dividing both sides by 3/3 (or 1) simplifies the equation:
49/7 = d

Therefore, the value of d is 49/7, which can be simplified to 7.