Question

If a line passes through the points (2,2) and (4,5), the equation of the line is 2=3/2(x-__)?

Answer 1

To find the equation of a line passing through two given points, we can use the slope-intercept form: y = mx + b. By finding the slope and substituting one of the points into the equation, we can determine the equation of the line passing through the given points.

Step-by-step explanation:

To determine the equation of a line passing through two points, we can use the slope-intercept form, which is y = mx + b. Here, m represents the slope of the line, and b represents the y-intercept.

First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). For the given points (2,2) and (4,5), the slope is (5 - 2) / (4 - 2) = 3/2.

Next, we can substitute the slope and one of the points into the equation (x1, y1) to find the value of b. Using (2,2): 2 = (3/2)(2) + b. Solving for b, we get b = -1.

Therefore, the equation of the line is y = (3/2)(x - 2) - 1.

Answer 2

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m =
`(5-2)/(4-2)` =
`(3)/(2)`

use either of the 2 points for (a, b)

Using (a, b) = (2, 2), then

y - 2 =
`(3)/(2)`(x - 2) ← equation of line