Question

What is the slope-intercept form of the equation with a slope of `4/3` and which goes through the point `(-2, -0)`?

Answer 1

See a solution process below:

Explanation:

We can use the point-slope formula to find the equation for this slope and point. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

First we can substitute the slope for `color(red)(m)` giving:

`y = color(red)(4/3)x + color(blue)(b)`

Next, we can substitute the values from the point in the problem and solve for `color(blue)(b)`:

`0 = (color(red)(4/3) xx -2) + color(blue)(b)`

`0 = -8/3 + color(blue)(b)`

`color(red)(8/3) + 0 = color(red)(8/3) - 8/3 + color(blue)(b)`

`8/3 = 0 + color(blue)(b)`

`8/3 = color(blue)(b)`

We can substitute `8/3` for `color(blue)(b)` and the slope from the problem to write the equation:

`y = color(red)(4/3)x + color(blue)(8/3)`