Question

Using the point-slope formula, what is the equation of the line that passes through the points (1, 5) and (0, 0)?

Answer 1

the answer is y=5x

Explanation:

we are using the slope-intercept form which is y=mx+b (m is the slope and b is the y-intercept) then we do Y2-Y1/ X2-X1 (this is to find the slope) 0-5= -5,0-1=-1.. -5/-1= 5 is our slope so the answer would be y=5x

Answer 2

point-slope form:
Given a point (x₀,y₀) and the slope "m", the point -slope form is :
y-y₀=m(x-x₀)

Given two points, (x₁,y₁) and (x₂,y₂) the slope can be:
m=(y₂-y₁) / (x₂-x₁)
or can be:
m=(y₁-y₂) / (x₁-x₂)

Therefore:
1) we calculate the slope:
(1,5)
(0,0)
m=(5-0)/(1-0)=5/1=5

2) Now, we calculate the equation of the line htan passes thorugh the pointes (1,5) and (0,0).

We take only one point, for example:
(0,0)
m=5

y-y₀=m(x-x₀)
y-0=5(x-0)
y=5x

answer: the line that passes through the points (1,5) and (0,0) is y=5x