Question

What is the y-intercept of a line with a slope of 2/3 that passes through (-5,1)?

Answer 1

(0,13/3)

Explanation:

The slope intercept form of a line is

y = mx+b

We know the slope is 2/3 and a point on the line is (-5,1)

y = 2/3x +b

Substitute the point into the equation

1 = 2/3 (-5) +b

1 = -10/3 +b

3/3 = -10/3 +b

Add 10/3 to each side

10/3 = b

The equation is

y = 2/3 x+13/3

The y intercept is

(0,13/3)

Answer 2

`(0,13/3)`

Explanation:

Since we know the slope and a point, we can use the point-slope form.

Recall that the point-slope form is:

`y-y_1=m(x-x_1)`

Let m be 2/3 and let (-5,1) be x₁ and y₁. Therefore:

`y-(1)=(2)/(3)(x-(-5))`

Simplify:

`y-(1)=(2)/(3)(x+5)`

Distribute:

`y-1=(2)/(3) x+(10)/(3)`

Add 1 to both sides. The left cancels. 1 is the same as 3/3:

`y=(2)/(3) x+(10)/(3)+(3)/(3)\\`

Simplify:

`y=(2)/(3)x+(13)/(3)`

This is in slope-intercept form. The coefficient is the slope and the y-intercept is the constant. Thus, the y-intercept is 13/3.