Question

What is the equation of a line that passes through (4,7) and has a slope of .5?

Answer 1

See a solution process below:

Explanation:

We can use the point slope formula to write an equation for this problem. The point-slope form of a linear equation is: `(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))`

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

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

`(y - color(blue)(7)) = color(red)(0.5)(x - color(blue)(4))`

If necessary, we can convert this to 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.

`y - color(blue)(7) = (color(red)(0.5) xx x) - (color(red)(0.5) xx color(blue)(4))`

`y - color(blue)(7) = 0.5x - 2`

`y - color(blue)(7) + 7 = 0.5x - 2 + 7`

`y - 0 = 0.5x + 5`

`y = color(red)(0.5)x + color(blue)(5)`