Question

A line passes through the point (2, 1) and has a slope of -5/2

Write an equation in slope-intercept form for this line.

Answer 1

To find the equation of the line with a given point (2, 1) and slope -5/2, you substitute the point into the slope-intercept formula, solve for y-intercept, and write the equation as y = (-5/2)x + 6.

Step-by-step explanation:

To write the equation of a line in slope-intercept form, we use the formula y = mx + b, where m is the slope and b is the y-intercept. Given the point (2, 1) and the slope -5/2, we can substitute the slope and the coordinates of the point into the slope-intercept form to find b.

Starting with the slope-intercept form:

y = mx + b

Substituting the given values:

1 = (-5/2)(2) + b

This simplifies to:

1 = -5 + b

Adding 5 to both sides to solve for b:

b = 6

With both m and b known, the equation of the line is:

y = (-5/2)x + 6

Answer 2

`y = -(5)/(2)x +6`

Step-by-step explanation:

Given

`m = -(5)/(2)` -- slope

`(x_1,y_1) = (2,1)` --- point

Required

Determine the line equation

In slope intercept form, a line equation is:

`y - y_1 = m(x - x_1)`

This gives:

`y - 1 = -(5)/(2)(x - 2)`

Open bracket

`y - 1 = -(5)/(2)x +5`

Add 1 to both sides

`y - 1+1 = -(5)/(2)x +5+1`

`y = -(5)/(2)x +6`