Question

How do you write a line with slope = 3; (1, 5) ?

Answer 1

See the entire solution process below:

Explanation:

We can use the point-slope formula to write an equation with the slope in the problem and going through the point in the problem. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

`(y - color(red)(5)) = color(blue)(3)(x - color(red)(1))`

We can also find the equation in slope-intercept form. 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.

Substituting the slope and the value from the point in the problem and solving for `b` gives:

`5 = (color(red)(3) * 1) + color(blue)(b)`

`5 = 3 + color(blue)(b)`

`-color(red)(3) + 5 = -color(red)(3) + 3 + color(blue)(b)`

`2 = 0 + color(blue)(b)`

`2 = color(blue)(b)`

Substituting this `2` for `b` and the slope from the problem into the formula gives the equation for the line as:

`y = color(red)(3)x + color(blue)(2)`