Question

In Progress Question Help X) 3.4.PS-7 Aline passes through the points (4,18) and (9,23). Write a linear function rule in terms of x and y for this line. The linear function rule is y= Enter your answer in the answer box and then click Check Answer. Clear All All parts showing Back Next → Question 1 of 9 Review progress

Answer 1

Equation of the line is

y = x + 14

Step-by-step explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

So, we just need to use the two points given to calculate the slope and use one of the points to then write the equation of the line.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For this question,

(x₁, y₁) and (x₂, y₂) are (4, 18) and (9, 23)

`\text{Slope = }(23-18)/(9-4)=(5)/(5)=1`

Recall that

y - y₁ = m (x - x₁)

m = Slope = 1

Point = (x₁, y₁) = (4, 18)

x₁ = 4, y₁ = 18

y - y₁ = m (x - x₁)

y - 18 = 1 (x - 4)

y - 18 = x - 4

y = x - 4 + 18

y = x + 14

Hope this Helps!!!