Question

What is the equation of a line that passes through the point (2, 4) and has a y-intercept at y = -10?

Answer 1

The equation of the line is y = 7x - 10

Explanation:

* Lets revise the form of the equation

- The form of the equation of a line is y = mx + c , where m is the slope

of the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

- The slope of the line which passes through points (x1 , y1) , (x2 , y2)

is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

* Lets solve the problem

∵ The y-intercept is y = -10

∴ The line intersects the y-axis at point (0 , -10)

∵ The line passes through the points (2 , 4) and (0 , -10)

- Lets find the slope of the line using the rule of the slope above

∵
`m=(-10-4)/(0-2)=(-14)/(-2)=7`

∴ The slope of the line is 7

∵ c is the y-intercept

∵ The y-intercept is y = -10

∴ c = -10

∵ y = mx + c

∴ y = 7x + -10

∴ y = 7x - 10

* The equation of the line is y = 7x - 10