Question

a line passes through (4, 5) and has a slope of 5/2. write an equation in slope intercept form for this line

Answer 1

To find the equation of a line in slope-intercept form given a point (4, 5) and a slope of 5/2: first plug the slope into the general form y = mx + b, then use the point to solve for b. In this case, b is -5. The final equation is y = (5/2)x - 5.

Step-by-step explanation:

To write the equation of a line in slope-intercept form (y = mx + b), you need two pieces of information: the slope (m) and the y-intercept (b). You have been given a point the line passes through, which is (4, 5), and the slope, which is 5/2.

First, let's use the slope-intercept form: y = mx + b. Plugging in the slope, we have y = (5/2)x + b. Now, we use the point to find b. Plug in x = 4 and y = 5 into the equation and solve for b:

5 = (5/2)(4) + b
5 = 10 + b
b = 5 - 10
b = -5

So, the y-intercept is -5. We can now write the final equation of the line:

y = (5/2)x - 5

Answer 2

The answer to your question is: y = 5/2 x - 5

Step-by-step explanation:

Data

P (4, 5)

slope = m = 5/2

Equation

(y - y1) = m(x - x1)

Process

1.- Substitute the data in the equation

(y - 5) = 5/2 (x - 4)

2.- Multiply 5/2 by the right terms

y - 5 = 5/2 x - 20/2

3.- Simplify

y = 5/2 x - 10 + 5

y = 5/2 x - 5