Question

A line includes the points (0, –6) and (–2, –10). What is its equation in slope-intercept form?

Answer 1

Answer:

y = 2x - 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, - 6 ) and (x₂, y₂ ) = (- 2, - 10 )

m = $\frac{-10-(-6)}{-2-0}$ = $\frac{-10+6}{-2}$ = $\frac{-4}{-2}$ = 2

The line crosses the y- axis at (0, - 6 ) ⇒ c = - 6

y = 2x - 6 ← equation of line

Answer 2

Answer:

y = 2x - 6

Step-by-step explanation:

The slope-intercept equation is y = mx + b

where m is the slope and b is the point on the y axis when x=0 which is called the y intercept.

The slope is the rise over run.

Rise is the difference in the y values.

Run is the difference in the x values.

Rise = difference between -6 and -10  which is 4 units

Run = difference between 0 and -2 which is 2 units.

The slope would then be 4 over 2 or 4/2 which can be reduced down to 2.

If you visualize the line on the graph, the line slopes upward from left to right.  So the slope must be a positive number.

Slope = 2

The y intercept is when x=0.  One of the coordinates (0, -6) gives you that answer.  When x=0, y = - 6.  This is b.

Your equation would be y = 2x - 6