Question

How do you find equation in slope intercept form of the straight line that has an x intercept of 5 & a y intercept of 10?

Answer 1

See the entire solution process below:

Explanation:

From the problem, because we were given the x and y-intercepts, we know two points on the line:

x-intercept = (5, 0) and y-intercept = (0, 10)

Knowing these points we can determine the slope. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting gives:

`m = (color(red)(10) - color(blue)(0))/(color(red)(0) - color(blue)(5)) = 10/-5 = -2`

We can now use the slope intercept formula to find the equation of the line. 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 again gives:

`y = color(red)(-2)x + color(blue)(10)`